In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.

We recently formulated Modular Dvoretzky, Type-Cotype, Khinchin-Kahane and Grothendieck Inequality problems in the Appendix of \textit{[arXiv:2302.03718v1]}. For the sake of wide accessibility we give a separate treatment of them.

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag–Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information.

Type-2 diabetes mellitus (T2DM) have been strongly associated with single nucleotide polymorphisms (SNPs) in the TCF7L2 gene. This study investigated the association between rs12255372, rs7903146 and T2DM in a Ghanaian population. A case-control study design was used for this study. A total of 106 T2DM patients and 110 control participants were selected. Basic data collected included body mass index, blood pressure and socio-demographics. Fasting blood samples were collected and used for serum lipid analysis, HbA1c, plasma glucose estimation and DNA extraction. Common and allele-specific primers were designed for genotyping using the Modified Tetra-Primer Amplification assay. Associations were evaluated using logistic regression models. The rs7903146 risk variant was significantly associated with 2.16 vs 4.06 increased odds for T2DM in patients <60 years vs ≥60 years. Both rs7903146 and rs12255372 are significantly associated with increased odds of T2DM in women, overweight/obese; T2DM negative family history (T2DM-NFH) and low-HDL-C. In a multivariate model, rs7903146 but not rs12255372 was significantly associated with 2.18, 5.01 and 2.25 increased odds of T2DM, under the codominant, recessive and additive model, respectively (p<0.05). The association between rs7903146 and rs12255372 with T2DM is more highly associated in a subgroup- women and those with T2DM-NFH, yet have cardiometabolic risk.

Advanced image processing will be crucial for emerging technologies such as autonomous driving, where the requirement to quickly recognize and classify objects under rapidly changing, poor visibility environments in real time will be needed. Photonic technologies will be key for next-generation signal and information processing, due to their wide bandwidths of 10’s of Terahertz and versatility. Here, we demonstrate broadband real time analog image and video processing with an ultrahigh bandwidth photonic processor that is highly versatile and reconfigurable. It is capable of massively parallel processing over 10,000 video signals simultaneously in real time, performing key functions needed for object recognition, such as edge enhancement and detection. Our system, based on a soliton crystal Kerr optical micro-comb with a 49GHz spacing with >90 wavelengths in the C-band, is highly versatile, performing different functions without changing the physical hardware. These results highlight the potential for photonic processing based on Kerr microcombs for chip-scale fully programmable high-speed real time video processing for next generation technologies.

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.

A construction for the systems of natural and real numbers is presented in Zermelo-Fraenkel Set Thoery, that allows for simple proofs of the properties of these systems, and practical and mathematical applications. A practical application is discussed, in the form of a Simple and Linear Fast Adder (Patent Pending). Applications to finite group theory and analysis are also presented. A method is illustrated for finding the automorphisms of any finite group $G$, which consists of defining a canonical block form for finite groups. Examples are given, to illustrate the procedure for finding all groups of $n$ elements along with their automorphisms. The canonical block form of the symmetry group $\Delta_4$ is provided along with its automorphisms. The construction of natural numbers is naturally generalized to provide a simple and sound construction of the continuum with order and addition properties, and where a real number is an infinite set of natural numbers. A basic outline of analysis is proposed with a fast derivative algorithm. Under this representation, a countable sequence of real numbers is represented by a single real number. Furthermore, an infinite $\infty\times\infty$ real-valued matrix is represented with a single real number. A real function is represented by a set of real numbers, and a countable sequence of real functions is also represented by a set of real numbers. In general, mathematical objects can be represented using the smallest possible data type and these representations are calculable. In the last section, mathematical objects of all types are well assigned to tree structures in a proposed type hierarchy.

Mesenchymal stem cells (MSCs) are involved in the process of extracellular matrix (ECM) remodeling where collagens play a pivotal role. We recently demonstrated that the remodeling of adsorbed collagen type I might be disordered upon oxidation following its fate in the presence of human adipose-derived MSC (ADMSCs). With the present study, we intended to learn more about the effect of polyphenolic antioxidant Epigallocatechin gallate (EGCG) attempting to mimic the conditions of oxidative stress in vivo and its putative prevention by antioxidants. Collagen Type I was isolated from mouse tail tendon (MTC) and labeled with FITC before oxidizing according to Fe2+/H2O2 protocol. FITC-collagen remodeling by ADMSC was assessed morphologically before and after EGCG pretreatment and confirmed via detailed morphometry analysis measuring the anisotropy index (AI) and fluorescence intensity (FI) in selected regions of interest (ROI), namely: outside the cells; over the cells and central (nuclear perinuclear) region, whereas the pericellular proteolytic activity was measured by de-quenching of fluorescent collagen probes (FRET effect). Here we provide morphological evidence that MTC undergoes significant reorganization by the adhering ADMSC along with the substantial activation of pericellular proteolysis, and further confirm that both processes are suppressed upon collagen oxidation. An important observation was that this abrogated remodeling cannot be prevented by the EGCG pretreatment. Conversely, the detailed morphometry analysis showed that oxidized FITC-collagen rather tends to accumulate beneath the cells and around the cell’s nuclei suggesting the activation of alternative routes for its removal, such as internalization and/or transcytosis. Morphometry analysis also revealed that both processes are supported by EGCG pretreatment.

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

In this paper, we design two inertial-type subgradient extragradient algorithms with line-search process for solving the pseudomonotone variational inequality problems (VIPs) and common fixed-point problem (CFPP) of finite Bregman relatively nonexpansive mapping and a Bregman relatively demicontractive mapping in p-uniformly convex and uniformly smooth Banach spaces, which are more general than Hilbert spaces. Under mild conditions, we derive weak and strong convergence of the suggested algorithms to a common solution of the VIPs and CFPP, respectively. Additionally, an illustrated example is furnished to back up the feasibility and implementability of our proposed methods.

Infant hepatitis B vaccine coverage in China is high, with over 95% of infants immunized; however, high vaccine coverage can often mask low timeliness. The vaccination interval between the second and third dose is not clearly defined by immunization guidelines in China. This retrospective cohort study assessed the time interval distribution of hepatitis B vaccination among a cohort of randomly selected live births from Centers for Disease Control and Prevention across four provinces or municipalities in China between January 2017 and December 2021. Among the infants analyzed, 163,224 received the first dose of hepatitis B vaccine with 146,905 (90.0%) and 135,757 (83.2%) infants receiving the second and third doses, respectively. A total of 132,577 (90.2%) infants received the second dose between 28–61 days after the first dose. Of the 119,437 (88.0%) infants that completed the hepatitis B series between 61–214 days after the second dose, 87,067 (64.1%) infants were vaccinated with the third dose between 151–180 days after the second dose. The time interval distribution for the three doses of hepatitis B vaccine varied across the four provinces or municipalities (P&lt;0.001). Of the 58,077 infants who completed the hepatitis B vaccine series, 36,377 (62.6%) infants used the same type of hepatitis B vaccine for all three doses. Overall, the timeliness of hepatitis B vaccination for infants was lower than expected, with regional disparities observed. This highlights the need for improved timeliness through the introduction of a defined timeframe for the last two doses of vaccine, and training for obstetricians and related personnel.

In this study, we prove the norm separating property for the composition of Cesàro 1 and Gamma matrices with their transpose. As a result, we compute the ℓp-norms of six classes of operators that commute with the infinite Hilbert operators. Additionally, we find the norm of 3 Hilbert’s commutants on some well-known sequence spaces.

In a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it.

Bianchi type III string cosmological models (massive and geometric) in presence of magnetic field with vacuum energy density following the techniques used by Letelier (1979) and Stachel (1980) are obtained. We find that the energy conditions (dominant as well as weak) given by Hawking and Ellis (1974) are satisfied for the models. Also the solutions obtained satisfy conservation equation for massive string with magnetic field and vacuum energy density. The models in general, represent anisotropic phase of space-time due to the presence of string. However, the models isotropize at late time and in special case. It has also been shown that the magnetic field is directly linked with the matter. For string dust model, the state finder parameters {r,s} are in excellent agreement with Planck results (Sahni et al. (2003)). The physical and geometrical aspects of the models with special cases are also discussed.

Let $\mathcal{X}$ be a Banach space. Let $\{\tau_j\}_{j=1}^n, \{\omega_k\}_{k=1}^m\subseteq \mathcal{X}$ and $\{f_j\}_{j=1}^n$, $\{g_k\}_{k=1}^m\subseteq \mathcal{X}^*$ satisfy $ |f_j(\tau_j)|\geq 1$ for all $ 1\leq j \leq n$, $|g_k(\omega_k)|\geq 1 $ for all $1\leq k \leq m$. If $x \in \mathcal{X}\setminus \{0\}$ is such that $x=\theta_\tau\theta_f x=\theta_\omega\theta_g x$, then we show that \begin{align}\label{FKDB} \|\theta_fx\|_0\|\theta_gx\|_0\geq \frac{\bigg[1-(\|\theta_fx\|_0-1)\max\limits_{1\leq j,r \leq n,j\neq r}|f_j(\tau_r)|\bigg]^+\bigg[1-(\|\theta_g x\|_0-1)\max\limits_{1\leq k,s \leq m,k\neq s}|g_k(\omega_s)|\bigg]^+}{\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|f_j(\omega_k)|\right)\left(\displaystyle\max_{1\leq j \leq n, 1\leq k \leq m}|g_k(\tau_j)|\right)}. \end{align} We call Inequality (\ref{FKDB}) as \textbf{Functional Kuppinger-Durisi-B\"{o}lcskei Uncertainty Principle}. Inequality (\ref{FKDB}) improves the uncertainty principle obtained by Kuppinger, Durisi and B\"{o}lcskei \textit{[IEEE Trans. Inform. Theory (2012)]} (which improved the Donoho-Stark-Elad-Bruckstein uncertainty principle \textit{[SIAM J. Appl. Math. (1989), IEEE Trans. Inform. Theory (2002)]}). We also derive functional form of the uncertainity principle obtained by Studer, Kuppinger, Pope and B\"{o}lcskei \textit{[EEE Trans. Inform. Theory, (2012)]}.

In the present paper we introduce the concept of orthogonal frames in Krein spaces, prove the independence of the choice of the fundamental symmetry, and from this we obtain a number of interesting properties that they satisfy. We show that there is no distinction between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert. Furthermore, we characterize frames dual to a given frame, which is a useful tool for constructing examples.

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on hyperbolic continuous manifolds, standing for the counterpart of QM’s Hilbert spaces. We describe how the tenets of QM, such as the observable A, the autostates ψa and the Schrodinger equation for the temporal evolution of states, might work very well on a Poincaré disk equipped with rotational groups. This curvature-based approach to QM, combined with the noncommutativity formulated in the language of gyrovectors, leads to a mathematical framework that might be useful in the investigation of relativity/QM relationships. Furthermore, we introduce a topological theorem, termed the punctured balloon theorem (PBT), which states that an orientable genus-1 surface cannot encompass disjoint points. PBT suggests that hyperbolic QM manifolds must be of genus ≥ 1 before measuring and genus zero after measuring. We discuss the implications of PBT in gauge theories and in the physics of the black holes.

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

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

Commuting is a vital travel channel for college students throughout their higher education career; nevertheless, excessive commute time negatively impacts students’ school satisfaction, academic achievement, health, and quality of life. Meanwhile, few studies have explored students’ commute time, covering a large population and scope. Therefore, this study analyzes the dwelling type that influences college and graduate students’ school commute times in the Seoul Metropolitan Area, using data from the 2016 Household Travel Diary Survey. This study uses spatial data on housing development to classify five dwelling types (i.e., new town, housing site development, Seoul, Incheon, and Gyeonggi-do). A multiple linear regression model empirically analyses students’ household and personal characteristics. The results reveal that dwelling type significantly affects students’ commute time. Specifically, Students living in Seoul have a shorter commute to school than those living in new towns. Socioeconomic characteristics have less effect on college and graduate students' school commute time. This study discusses the problem of excessive commuting of college and graduate students in new towns.

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that $\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t. p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$ w.r.t. p-norm, then we show that \begin{align}\label{ME} &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ &o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta, 0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequalities (\ref{ME}) and (\ref{ME2}) as \textbf{Functional Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (\ref{ME}) and (\ref{ME2}) improve the finite approximate support uncertainty principle obtained by Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} o(M)^\frac{1}{q}o(N)^\frac{1}{p}< \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}, \end{align*} where $q$ is the conjugate index of $p$. Then for all $x \in \mathcal{X}$, we show that \begin{align}\label{FGJU} (1) \quad \quad \quad \quad \|x\|\leq \left(1+\frac{1}{1-o(M)^\frac{1}{q}o(N)^\frac{1}{p}\displaystyle\max_{1\leq j,k\leq n}|g_k(\tau_j)|}\right)\left[\left(\sum_{j\in M^c}|f_j(x)|^p\right)^\frac{1}{p}+\left(\sum_{k\in N^c}|g_k(x) |^p\right)^\frac{1}{p}\right]. \end{align} We call Inequality (1) as \textbf{Functional Ghobber-Jaming Uncertainty Principle}. Inequality (1) improves the uncertainty principle obtained by Ghobber and Jaming \textit{[Linear Algebra Appl., 2011]}.

The aim of this paper is to determine a suitable definition for the concept of fuzzy Hilbert space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Then we considered another approach to the notion of fuzzy inner product and analysed its properties.

Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to device suitable applications. This article aims to propose for the first time an approach to use quantum logic in image processing at hand of a process for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables to initiate the principal component analysis. At hand of experiments, we explore the possibility to distinguish between different geometrical objects and discuss the results in terms of quantum logical interpretation.

In this article key results in general relativity are studied and the dynamics of quantum fields in curved spacetime is reviewed. It has been shown geometrically how dark energy breaks strong energy condition. We study tan-hyperbolic inflation for an open FRWL universe and show that over half and full period scalar field remains in it's initial state.

We specify basic definitions of the Chern-Simons current in cohomology theory, then we calculate its value by using a model of quantum machine learning, the so-called supersymmetric support Dirac machine. The supercurrent is generated from the coupling between three states of a quantum flux of modified Wilson loop of the Cooper pairs. We use Holo-Hilbert spectrum in frequency modulation to visualize the network as a coupling behavior of convolutional neuron network in superstatistical theory with the application to the theory of a superconductor. We also calculate the number of carbon atoms in the stable support spinor network structure of a graphene wormhole to produce a supercurrent of Cooper pairs as graviphoton states by using the Holo-Hilbert spectral analysis.

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, particularly susceptible to instability. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By contrasting empirical correlations with those derived from random matrices, we uncover non-random properties and underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Let $\{f_j\}_{j=1}^n$ and $\{g_k\}_{k=1}^m$ be Parseval p-frames for a finite dimensional Banach space $\mathcal{X}$. Then we show that \begin{align}\label{UE} \log (nm)\geq S_f (x)+S_g (x)\geq -p \log \left(\displaystyle\sup_{y \in \mathcal{X}_f\cap \mathcal{X}_g, \|y\|=1}\left(\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(y)g_k(y)|\right)\right), \quad \forall x \in \mathcal{X}_f\cap \mathcal{X}_g, \end{align} where \begin{align*} &\mathcal{X}_f\coloneqq \{z\in \mathcal{X}: f_j(z)\neq 0, 1\leq j \leq n\}, \quad \mathcal{X}_g\coloneqq \{w\in \mathcal{X}: g_k(w)\neq 0, 1\leq k \leq m\},\\ &S_f (x)\coloneqq -\sum_{j=1}^{n}\left|f_j\left(\frac{x}{\|x\|}\right)\right|^p\log \left|f_j\left(\frac{x}{\|x\|}\right)\right|^p, \quad S_g (x)\coloneqq -\sum_{k=1}^{m}\left|g_k\left(\frac{x}{\|x\|}\right)\right|^p\log \left|g_k\left(\frac{x}{\|x\|}\right)\right|^p, \quad \forall x \in \mathcal{X}_g. \end{align*} We call Inequality (1) as \textbf{Functional Deutsch Uncertainty Principle}. For Hilbert spaces, we show that Inequality (1) reduces to the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We also derive a dual of Inequality (1).

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^m, \{\omega_k\}_{k=1}^m)$ be p-Schauder frames for a finite dimensional Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}\label{UE} \|\theta_f x\|_0^\frac{1}{p}\|\theta_g x\|_0^\frac{1}{q} \geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(\omega_k)|}\quad \text{and} \quad \|\theta_g x\|_0^\frac{1}{p}\|\theta_f x\|_0^\frac{1}{q}\geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|g_k(\tau_j)|}. \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^m \in \ell^p([m]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (\ref{UE}) as \textbf{Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality (\ref{UE}) improves Ricaud-Torr\'{e}sani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

\textsc{Background} Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. Currently, a major problem in biology is to cherry pick the combinations based on expert advice, literature survey or guesses for investigation. The search and wet lab testing of these combinations costs a lot in terms of time, investment and energy. In a recent development of the PORCN-WNT inhibitor ETC-1922159 for colorectal cancer, a list of down-regulated genes were recorded in a time buffer after the administration of the drug. The regulation of the genes were recorded individually but for a majority, it is still not known which higher ($\geq 2$) order combinations might be playing a greater role in the pathway. \textsc{Results} The pipeline provides a prioritised list of important $2^{nd}$ order combinations of a range of family of genes involved in the Wnt pathway. More specifically, it reveals the various unexplored FZD-WNT combinations that have been untested till now in the pathway. In relation to ETC-1922159 affected combinations, the down-regulation of LGR-RNF family after the drug treatment is evident in these rankings as it takes bottom priorities for LGR5-RNF43 combination. The LGR6-RNF43 takes higher ranking than LGR5-RNF43, indicating that it might not be playing a greater role as LGR5 during the Wnt enhancing signals. These rankings confirm the efficacy of the proposed search engine design. \textsc{Conclusion} A pipeline has been developed to prioritise an $n^{th}$ order combination of factors that affect a signaling pathway. It takes into account the sensitivity indices computed from variance based (SOBOL) and density-kernel based (HSIC) methods to estimate the influence of each factor or combination of factors. These are then fed as feature vectors into a powerful support vector ranking algorithm that produces a ranked list of the interactions/combinations.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces and $\{\tau_\alpha\}_{\alpha\in \Omega}$, $\{\omega_\beta\}_{\beta \in \Delta}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align}\label{UE} \log (\mu(\Omega)\nu(\Delta))\geq S_\tau(h)+S_\omega (h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{\alpha \in \Omega, \beta \in \Delta}|\langle\tau_\alpha , \omega_\beta\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_\tau \cap \mathcal{H}_\omega, \end{align} where \begin{align*} &\mathcal{H}_\tau := \{h_1 \in \mathcal{H}: \langle h_1 , \tau_\alpha \rangle \neq 0, \alpha \in \Omega\}, \quad \mathcal{H}_\omega := \{h_2 \in \mathcal{H}: \langle h_2, \omega_\beta \rangle \neq 0, \beta \in \Delta\},\\ &S_\tau(h):= -\displaystyle\int\limits_{\Omega}\left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\,d\mu(\alpha), \quad \forall h \in \mathcal{H}_\tau, \\ & S_\omega (h):= -\displaystyle\int\limits_{\Delta}\left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\,d\nu(\beta), \quad \forall h \in \mathcal{H}_\omega. \end{align*} We call Inequality (\ref{UE}) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (\ref{UE}) improves the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We formulate Kraus conjecture for 1-bounded continuous Parseval frames. We also derive continuous Deutsch uncertainty principles for Banach spaces.

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought.

The unexploited unification of quantum physics, general relativity and biology is a keystone that paves the way towards a better understanding of the whole of Nature. Here we propose a mathematical approach that introduces the problem in terms of group theory. We build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses the three frameworks as subsets, representing two of their most dissimilar experimental results, i.e., 1) the commutativity detectable both in our macroscopic relativistic world and in biology; 2) and the noncommutativity detectable both in the microscopic quantum world and in biology. This approach leads to a mathematical framework useful in the investigation of the three apparently irreconcilable realms. Also, we show how cyclic groupoids encompassing quantum mechanics, relativity theory and biology might be equipped with dynamics that can be described by paths on the twisted cylinder of a Möbius strip.

Abstract: The study used whole-genome sequencing (WGS) and bioinformatics analysis for the genomic characterization of 60 isolates of Listeria monocytogenes isolated from cattle farms, cattle abattoirs, and retail outlets in Gauteng province, South Africa. The isolates' sequence types (STs), clonal complexes (CCs), and lineages were determined using in silico multilocus sequence typing (MLST). We used BLAST-based analyses to identify virulence and antimicrobial genes, plasmids, proviruses, and the CRISPR-Cas system. The study investigated any association of the detected genes to the origin in the beef production chain of the L. monocytogenes isolates. Overall, in 60 isolates of Listeria monocytogenes, there were 7 STs, 6 CCs, 44 putative virulence factors, 2 resistance genes, 1 plasmid with AMR genes and 3 with conjugative genes, 1 CRISPR gene, and all 60 isolates were positive for proviruses. Among the 7 STs detected, ST204 (46.7%) and ST2 (21.7%) were the most prominent, with ST frequency varying significantly (p&lt;0.001). The predominant CC detected were CC2 (21.7%) and CC204 (46.7%) in lineages I and II, respectively. Of the 44 virulence factors detected, 26 (across Listeria Pathogenicity Islands, LIPIs) were present in all the isolates. The difference in the detection frequency varied significantly (P&lt;0.001). The two AMR genes (fosX and vga(G)) detected were present in all 60 (100%) isolates of L. monocytogenes. The only plasmid, NF033156, was present in 3 (5%) isolates. A CRISPR-Cas system was detected in 6 (10%), and all the isolates carried proviruses. Significant differences were detected in the frequencies of STs and virulence factors regarding the source and sample type of the L. monocytogenes isolates. The presence of both fosX and vga(G) genes in all the isolates from the three industries (cattle farms, abattoirs, and retail outlets) can potentially cause therapeutic implications. Our study, which characterized L. monocytogenes recovered from the three levels in the beef production chain in the country, provides the first evidence of the distribution of the pathogen with potential food safety and therapeutic implications.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

Since atopic dermatitis (AD) is a heterogeneous condition, subtyping of AD is a crucial issue. The classical subtypes of AD are represented by extrinsic and intrinsic subtypes, European American and Asian subtypes, and adult and pediatric subtypes. While subtyping of AD was historically conducted based on the phenotype, recent findings on the mechanisms of AD have revealed importance of the endotype, which can characterize individual patients more accurately. Considering the current development of AD therapies, AD endotyping is prerequisite for personalized therapeutic choice. Endotypes of AD can be stratified from different viewpoints, including cytokine expression patterns, allergen properties, epidermal barrier conditions, ceramide variation, involvement of innate immunity, and serum biomarkers. Among them, the cytokine-based endotype seems to be the most useful one and is categorized into type 2 cytokine (IL-4, IL-13 and IL-31)-high, type 1 cytokine (interferon-g)-high, and/or type 3 cytokine (IL-22 and IL-17)-high, or mixed subtypes. The recently biomarker-proposed endotyping aims at individualized treatment options, although the daily clinical use of endotypes is a future issue. To better understand the endotypes for clinicians, attempts to adjust each of the classical subtypes to the endotypes are required. This review will discuss the correspondence of the classical subtypes to the various endotypes that have recently been proposed.

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

As an implementation of inverse Radon transform, the Second-order Divided-difference Back Projection (SDBP) technique has been proposed in this paper, by which the accurate CT reconstruction can be theoretically realized. A computational model for CT reconstruction filter expressions has been derived on the basis of SDBP technique. The method reveals the correlation between the convolution kernel for data restoration and the filter expression. By substituting kernel functions into the computational model, the amplitude sequences of a variety of filters can be calculated. On the proposed filter construction method, the decomposition form of filters has been discovered, where a series of basic filters have been acquired. The properties of any filter depend on the decomposed basic filters. Basic filters can be used to compose filters in actual needs.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

The switch from intermittently scanned continuous glucose monitoring (isCGM) to real-time (rt) CGM could improve glycemic management in suboptimal controlled type 1 diabetes patients, but long-term study is lacking. We evaluated retrospectively the ambulatory glucose profile (AGP) in such patients after switching from Free Style libre 1 (FSL1) to Dexcom G4 (DG4) over 1 year. Patients (n=21, 43±15 years, BMI 25±5, HbA1c 8.1±1.0%) had severe hypoglycemia and/or HbA1c≥8%. AGP metrics (time-in-range (TIR) 70-180 mg/dL, time-below-range (TBR)<70 mg/dL or <54 mg/dL, glucose coefficient of variation (%CV), time-above-range (TAR) >180 mg/dL or >250 mg/dL, glucose management indicator (GMI), average glucose) were collected the last 3 months of FSL1 use (M0) and of DG4 for 3, 6 (M6) and 12 (M12) months of use. Values were means ± standard deviation or medians [Q1;Q3]. At M12 versus M0, the higher TIR (50±17 vs. 45±16, P=0.036), and lower TBR<70 mg/dL (2.5 [1.6;5.5] vs. 7.0 [4.5;12.5], P=0.0007), TBR<54 mg/dL (0.7 [0.4;0.8] vs. 2.3 [0.8;7.0], P=0.007) and %CV (39±5 vs. 45±8, P=0.0009), evidenced a long-term effectiveness of the switch. Compared to M6, TBR<70mg/dL decreased, %CV remained stable, while the improvement on hyperglycemia exposure decreased (higher GMI, TAR and average glucose). This switch was a relevant therapeutic option, though a loss of benefit on hyperglycemia stressed the need for optimized management of threshold alarms. Nevertheless, few patients attained the recommended values for AGP metrics, and the reasons why some patients are “responders” vs “non-responders” warrant to be investigated.

This study tested the association between FecXG point mutation located in exon 2 of BMP15 gene and the prolificacy of Dubasi, Shugor and Watish sheep ecotypes, under dryland farming, Sudan. Blood samples were randomly collected from unrelated 100 ewes (Dubasi; n= 30, Shugor: n= 30, and Watish: n= 40). Bone Morphogenetic protein (BMP15) gene was amplified using PCR-RFLP. Two genotypes were found in all studied breeds (heterozygous and wild type). The calculated total genotype frequencies of BB, Bb and bb genotypes were 0.31, 0.69 and 0.00, respectively, while allele frequencies were 0.66 for B and 0.34 for b. Litter size was influenced by the genotypes of BMP15 gene, parities and subtypes (p<0.05), highest for Watish and 4th parity. Alignment of BMP15 samples along with database reference sequence revealed that most sequence regions were identical except for one variable nucleotide at position 111 bp where a guanine (G) was replaced by adenine (A) in Watish and Shugor samples. All amino acids were the same at residue 275. Watish and Shugor breeds are more related. The study concluded that the presence of one copy of FecXG point mutation of BMP15 gene increased the litter size by 0.17 lambs in the studied ecotypes.

To enhance the overall reliability of the power system, engineers have redirected their focus toward health monitoring and early detection of faults in transformers. Among these faults, transformer core defects demand particular attention. While fault simulation using software has traditionally been the preferred approach, these methods suffer from data inaccuracies in real-world conditions. Consequently, conducting actual experimental setups with induced faults is imperative to investigate core issues. This study uses Hilbert Transform (HT) as a signal processing technique to extract crucial data characteristics, thereby enhancing the performance of the classifier model. The research involves analyzing electric current signals from a single-phase 1kVA transformer. A comparative assessment of our proposed model was conducted using raw data and Fast Fourier Transform (FFT), evaluating accuracy, precision, recall, F1-score, and computational time. The results demonstrate a significant improvement in all metrics for the classifier models, particularly the k-nearest neighbor (KNN) algorithm, which exhibited values of 83.89%, 84.39%, 83.89%, 83.79%, and 0.0156 seconds, respectively. Future work aims to extend this analysis under different loading conditions.

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

This work reports the role of structure and composition on the determination of the performances of p-type SnOx TFTs deposited by rf magnetron sputtering at room temperature, followed by a post-annealed step up to 200 °C at different oxygen partial pressures (Opp), between 0% and 20%, but where the p-type conduction was only observed between 2.8–3.8%. The role of structure and composition were evaluated by XRD and Mössbauer spectroscopic studies. The study allows to identify the best phases/compositions and thicknesses (around 12 nm) to be used that lead to the production of TFTs with a bottom gate configuration, on glasses coated with conductive Indium Tin Oxide, followed by Aluminium Titanium Oxide dielectric layer with saturation mobility of 4.6 cm²V⁻¹s⁻¹ and on-off ratio above 7 × 10⁴, operating at the enhancement mode with a saturation voltage of −10 V.

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

To address the problem of limited fault diagnosis accuracy in oil-immersed on-load tap changers (OLTC), this paper introduces a novel fault diagnosis method that combines the analysis of mechanical vibration signals and high-frequency current signals. The proposed approach aims to enhance the accuracy of fault diagnosis. To begin, an experimental platform is constructed to simulate the OLTC contact. Mechanical vibration signals and high-frequency current signals are collected from the testing platform under various operating states. These signals are then subjected to wavelet packet transform for denoising, followed by correlation analysis to capture the relationship between signals in different states. Based on these preliminary steps, the features of the signals are extracted and analyzed using ensemble empirical mode decomposition and the Hilbert-Huang transform. Subsequently, a support vector machine (SVM) is employed to analyze both the mechanical vibration signal and high-frequency current signal, enabling the classification of the OLTC contact state. The results demonstrate that the combination of characteristic analysis of mechanical vibration signals and high-frequency current signals provides a more comprehensive reflection of the actual OLTC contact state under different conditions. Through the SVM classification, the error between the predicted values and real values of the two types of signals remains below 10%, validating the efficiency and feasibility of the proposed method for fault diagnosis of OLTC contacts. These research findings serve as a reliable foundation for the diagnosis of operational states of on-site oil-immersed on-load tap changers, offering valuable insights for practical applications.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

Let $m$ and $n$ be the fixed positive integers. Suppose $\mathcal{A}$ is a von Neuman algebra with no central summands of type $I_{1}$ and $L_{m}$ be a Lie type higher derivation i.e., an additive (linear) map $L_{m} :\mathcal{A}\to \mathcal{A}$ such that \begin{equation}\label{def2} \[L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\] %L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\nonumber \end{equation} for all $\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}\in \mathcal{A}$. In the present paper, we study Lie type higher derivations on von Neuman algebras and prove that every additive Lie type higher derivation on $\mathcal{A}$ has a standard form at zero product as well as at projection product. Further, we discuss some more related results.

The genome of Vibrio cholerae contains three structural genes for the NhaP-type cation-proton antiporter paralogues, Vc-NhaP1, 2 and 3 mediating exchange of K+ and or Na+ for protons across the membrane. Based on phenotype analysis of chromosomal Vc-NhaP1, 2 and 3 triple deletion mutants we suggested that Vc-NhaP paralogues might play a role in the Acid Tolerance Response (ATR) of V. cholerae as it passes through the gastric acid barrier of the stomach. Comparison of the biochemical properties of Vc-NhaP isoforms revealed that Vc-NhaP2 is the most active among all three paralogues. Therefore, Vc-NhaP2 antiporter is a plausible therapeutic target for developing novel inhibitors targeting these ion exchangers. Our structural and mutational analysis of Vc-NhaP2 identified a putative cation binding pocket formed by antiparallel extended regions of two transmembrane segments (TMSs V/XII) along with TMS VI. Molecular Dynamics (MD) simulations suggested that the flexibility of TMS-V/XII is crucial for the intra-molecular conformational events in Vc-NhaP2. In this study, we developed some putative Vc-NhaP2 inhibitors from Amiloride analogs (AAs). Amiloride is a potent inhibitor of human Na+/H+ exchanger-1 (NHE1). Based on the pharmacokinetic properties and potential binding affinity scores we chose six AAs showing high binding affinity scores to Vc-NhaP2. In silico, the six AAs interacted with the functionally important amino acid residues located in TMSs III, IV, V, VI, VIIII and IX either from the cytoplasmic side (three AAs) or the periplasmic side (three AAs) of Vc-NhaP2. Four AAs were modified to reduce their toxicity profile compared to the original AAs. Molecular docking of the modified AAs revealed promising binding. The four selected drugs interacted with functionally important amino acid residues located on the cytoplasmic side of TMS VI, the extended chain region of TMS V and TMS XII and the loop region between TMSs VIIII and IX. Molecular dynamics simulations revealed that binding of the selected drugs destabilized the Vc-NhaP2 and altered the flexibility of functionally important TMS VI.

Recent reports suggest that the clinical course of coronavirus disease 2019 (COVID-19) in previously healthy children is usually milder as compared to adults. However, children with comorbid conditions such as diabetes are at increased risk of infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) as well as morbidity and mortality due to COVID-19. Experience in adults with diabetes shows that they are prone to faster metabolic decompensation, develop diabetes-related complications, and have a poor prognosis when hospitalized with COVID-19. Data on children are limited. The aim of this mini-review is to discuss the possible risks to children and adolescents with diabetes during the current pandemic and the special considerations in management in those affected with COVID-19. The challenges for children who develop new-onset type 1 diabetes during the COVID-19 lockdown, especially in accessing healthcare, are also discussed.

Fiber-rich green river Aonori alga is mass-cultivated in Japan; it has been reported to reduce inflammation and improve metabolic health in humans. Peroxisome proliferation-activated receptor (PPARs) are associated with metabolic disorders such as obesity and type 2 diabetes (T2DM). We evaluated the effects of supplementation with NBF2, a formula made of algal and junos citrus biomaterials, on metabolic markers in obese and diabetic rats. An experimental study was performed using 18 obese and hyperglycemic Otsuka Long-Evans Tokushima Fatty (OLETF) rats randomly assigned to high dose NBF2 (20mg/kg; n=6), low dose (10mg/kg; n=6) NBF2 drink for 6 weeks, whereas OLETF control rats received similar amount of tap water (vehicle; n=6). LETO rats were used as normal controls (n=8). Biospecimens were taken for ELISA and real-time PCR. Both high dose and low dose NBF2 increased brown adipose tissue (BAT) mass and adiponectin (APN), improved insulin sensitivity, and significantly improved glycemic and lipid (TG, LDL-c) profiles in NBF2-supplemented OLETF rats after a 6-week supplementation with NBF2 (vs. OLETF controls), as well as LDL-c (p<0.05). During the glucose tolerance test (OGTT), both NBF2 groups and LETO rats had normal glycemia by 90-minute time-point (vs. OLETF controls; p<0.01). Furthermore, intake of NBF2 up-regulated PPARa/g-mRNA and Sirt2-mRNA gene expressions in BAT, and improved blood pressure profile in OLETF rats. Findings from this research suggest that intake of NBF2 formula induces dual PPAR-a/g and Sirt2 activation, providing insights on beneficial prophylactic and therapeutic effects of this NB2 formula on dyslipidemia and hyperglycemia in T2DM.

We have investigated the interfacial dislocations in InxGa1–xN/GaN (0 ≤ x ≤ 0.20) heterostructures using diffraction contrast analysis in a transmission electron microscopy. The analysis indicate that the structural properties of the interface dislocations depend on the indium composition. For lower indium composition up to x = 0.09, we observed that the screw-type dislocations and dislocation half loops occurred at the interface even though the former do not contributes toward elastic relaxation of the misfit strain in the InGaN layer. With the increase of indium composition (0.13 ≤ x ≤ 0.17), in addition to the network of screw-type dislocations, edge-type misfit dislocations were found generated with their density gradually increasing. For higher indium composition (0.18 ≤ x ≤ 0.20), all the interfacial dislocations are transformed into a network of straight misfit dislocations along the <10-10> directions leading to partially relaxation of the InGaN epilayer. The presence of dislocation half loops may be explained by slip on the basal plane, the formation of misfit dislocations are attributed to punch-out mechanism.

Should our planet be visited by an extraterrestrial civilization, the prevailing assumption would undoubtedly be that the extraterrestrial civilization is Type I i.e. its capacity for interstellar travel results from its technological development. This assumption is dangerous for it unnecessarily leads to the Extraterrestrial Tandem Hypothesis (ETH): the belief than an extraterrestrial civilization technologically capable of interstellar travel must also be technologically compatible with the inexorably rapid annihilation of life on Earth. Such a state of things would compromise the planet’s capacity to stage a confident defense should the extraterrestrials prove belligerent. The presumption of Type I extraterrestrials (on the premise of the capacity for interstellar travel alone) is unfounded as extraterrestrials may be Type II i.e. capable of interstellar travel by virtue of natural intrinsic or extrinsic factors. This paper advances, most importantly, that the fundamental policy of first contact should be the employment of various strategies toward the evaluation of the technological capacity of visiting extraterrestrials. This evaluation must be particularly devoted to the detection of Type II extraterrestrials masquerading as Type I (using concealment and Wizard of Oz strategies). Integral to this detection are the concepts of the precedence relation and The Extraterrestrial Exclusion Principle (EEP). A precedence relation is a qualitative relation expressing the relative difficulty of producing a technological action. The Extraterrestrial Exclusion Principle states that a Type I extraterrestrial life form is excluded from certain actions. Such actions are lower in precedence than interstellar travel and may be described as in violation of the EEP or EEP forbidden. EEP actions reveal extraterrestrials to be Type II. As an example, the value of the Hawking Warning is subjected to EEP analysis. Furthermore, a hypothetical conundrum in linguistics termed the Kryptonian Linguistic Paradox (KLP) is discussed as a case of an EEP forbidden act. Finally, the paper explores the limitations of the stated fundamental policy of first contact.

Abstract: Several publications have raised the issue that the development of diabetes is preceded by alteration of the microbiome (dysbiosis) and hence, the role of environmental factors, triggering dysbiosis, should be considered. Antibiotics are powerful agents inducing dysbiosis and the authors wanted to explore the possible relationship between the consumption of different major classes of antibiotics and the prevalence of diabetes (type-1, /T1D/, type-2 /T2D/) in thirty European countries. According to our hypothesis, if such association exists, the dominant use of certain major antibiotic classes might be reflected in the prevalence of T1D and T2D in different countries. Comparisons were performed between the prevalence of diabetes (T1D and T2D) estimated for 2019 and featured in the Diabetes Atlas with the average yearly consumption of major antibiotic classes of the previous 10 years (2010-19) extracted from the ECDC yearly reports on antibiotic consumption in Europe. Pearson correlation and variance analysis were used to estimate the possible relationship. Strong, positive (enhancer) associations were found between the prevalence of T1D and the consumption of tetracycline (J01A /p: 0.001/) and the narrow spectrum penicillin (J01CE /p: 0,006/, CF /p: 0.018/). Strong negative (inhibitor) association was observed with broad-spectrum, beta-lactamase resistant penicillin (J01CR /p: 0.003/), macrolide (J01F /p: 0.008/) and quinolone (J01M /p: 0.001/). T2D showed significant positive associations with cephalosporin (J01D /p: 0.048/) and quinolone (J01M /p: 0.025/), and a non-significant negative association was detected with broad-spectrum, beta-lactamase-sensitive penicillin (J01CA /p: 0.67/). Countries with the highest prevalence of diabetes (first 10 positions) showed concordance with the higher consumption of “enhancer” and the lower consumption of “inhibitor” antibiotics (first 10 positions) as indicated by variance analysis. Countries with high prevalence of T1D showed high consumption of tetracycline (p: 0.015), and narrow spectrum, beta-lactamase sensitive penicillin (p: 0.008), and low consumption of “inhibitor” antibiotics (broad-spectrum, beta-lactamase resistant, combination penicillin (p: 0.005), cephalosporin (p: 0.036), and quinolone (p: 0.003). Countries with a high prevalence of T2D consumed more cephalosporin (p: 0.084), quinolone (p: 0.54), and less broad-spectrum, beta-lactamase sensitive penicillin (p: 0.012) than other countries. Conclusion/Interpretation: The development of diabetes-related dysbiosis might be attached to higher consumption of specific classes of antibiotics, showing positive (enhancer) associations with the prevalence of diabetes, and the low consumption of other classes of antibiotics shoving negative (inhibitory) associations. Those groups of antibiotics are different in T1D and T2D

The incidence of Type 1 Diabetes (T1D) in the Arab world, particularly, oil and gas rich Gulf Cooperative Council (GCC) countries has more than doubled in the last twenty years. Therefore, there is a dire need for careful systematic familial cohort studies, especially in high-risk populations. Several immunogenetic factors affect the pathogenesis of the disease. Genes in the human leukocyte antigen (HLA) account for the major genetic susceptibility to the disease. The triggering agents initiate disease onset by destruction of pancreatic β-cells. The autoantibodies against glutamic acid decarboxylase (GADA), insulinoma antigen-2 (IA-2A), insulin (IAA), and zinc transporter-8 (ZnT-8A) comprise the most reliable biomarkers for T1D in both children and adults. Although three of the GCC countries, namely Kuwait, Saudi Arabia and Qatar are among the top 10 countries with high incidence rate of T1D, no proper diagnostic and prediction tools were applied in the region. Understanding the disease sequelae in a homogenous gene pool with high consanguinity in the GCC could help solve the challenges in understanding pathogenesis, as well as hasten the prevention of T1D. Arab states must incorporate T1D predictive and intervention policies on a war-footing basis to minimize the burden of this serious disease.

The mechanisms underlying the effects of γ-globulin therapy for bacterial infections are thought to involve bacterial cell lysis via complement activation, phagocytosis via bacterial opsonization, toxin neutralization, and antibody-dependent cell-mediated cytotoxicity. Nevertheless, recent advances in the study of pathogenicity in gram-negative bacteria have raised the possibility of an association between γ-globulin and bacterial toxin secretion. Over time, new toxin secretion systems like the type III secretion system have been discovered in many pathogenic gram-negative bacteria. With this system, the bacterial toxins are directly injected into the cytoplasm of the target cell through a special secretory apparatus without any exposure to the extracellular environment and, therefore, with no opportunity for antibodies to neutralize the toxin. However, because antibodies against the V-antigen, which is located on the needle-shaped tip of the bacterial secretion apparatus, can inhibit toxin translocation, this raises the hope that the toxin might be susceptible to antibody targeting. Because multi-drug resistant bacteria are now prevalent, inhibiting this secretion mechanism is attractive as an alternative or adjunctive therapy against lethal bacterial infections. Thus, it would not be unreasonable to define the blocking effect of anti-V-antigen antibodies as the fifth mechanism for immunoglobulin action against bacterial infections.

The Polyurethane (PU) mixture is a high−performance engineering material with different dynamic properties compared to a hot−mixed asphalt mixture (HMA). This paper analyzed whether the Kramers−Kronig (K−K) relation and thermo−rheological simple properties were applicable to the PU mixture. Based on the result discussion, the PU mixture exhibited thermo−rheological simple properties within the test conditions. The time−temperature superposition principle (TTSP) was applicable for the PU mixture to construct the dynamic modulus master curve using the standard logistic Sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak−Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The Core−Core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K−K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results. The phase angle of the PU mixture cannot be derived from the dynamic modulus data and currently needs to be derived from the laboratory measurement.

Gastric-type endocervical adenocarcinoma (GAS) is a rare non-human papillomavirus associated mucinous adenocarcinoma of the cervix. Its clinical manifestations are extremely atypical, with hidden lesions and difficulty in obtaining materials, resulting in a low positive rate of screening and biopsy. The pathological morphological features are similar to benign lesions, but the biological characteristics are highly malignant, posing great challenges to diagnosis. The preoperative diag-nostic rate is low, which is prone to misdiagnosis and missed diagnosis, leading to delayed treatment and seriously affecting the prognosis of patients. Here，we reported a case of ovarian endometriosis cyst combined with GAS confirmed by surgery and postoperative pathology, with "pelvic mass" as the initial symptom. Through case report and literature review, the characteristics and current re-search progress of GAS were summarized, in order to provide references for diagnosis of GAS, and provide theoretical guidance for formulating reasonable treatment strategy and improving patient prognosis.

Background: Over the past years, there has been a rise in the incidence of type 1 diabetes, partic-ularly among younger individuals. This concerning trend has prompted investigations into po-tential contributing factors, with intestinal dysbiosis emerging as a likely culprit for the escalating annual rates of the disease; (2) Methods: We conducted a retrospective ecologic correlational study involving 37 children from the southern region of Romania between 2019-2021. All participants were within the first six months following the onset of the disease; (3) Results: In the microbiota of the patients we observed a dysbiosis marked by an overabundance of bacteria (Clostridium coccoides, Faecalibacterium, Bacterioides, Enterobacteriaceae) and fungi, compared to the healthy control group. The Spearman correlation revealed a positive association between the presence of Bacteroides (p=0.0442), Butyricicoccus (p=0.0164), and Clostridium leptum (p=0.0023) with recent diabetes onset. Furthermore, a significant correlation was observed between younger age at onset and the pres-ence of Butyricicoccus (p=0.019). The use of antibiotics in the month preceding admission was linked to the presence of fungi in the microbiota (Candida, p=0.0442); (4) Conclusions: The dysbiosis of Romanian type 1 diabetes children correlates with inflammation, more severe onset of the disease and other au-toimmune diseases.

Type 2 diabetes mellitus (T2DM) is a polygenic metabolic disease described by hyperglycemia, which is caused by insulin resistance or reduced insulin secretion. Interaction between various genetic variants and environmental factors triggers T2DM. The main aim of this study was to find the risk associated with genetic variant (rs5210) of KCNJ11gene in the development of T2D in Indian Population. A total number of 300 cases of T2D and 100 control samples were studied to find the polymorphism in KCNJ11 through PCR-RFLP. The genotype and allele frequencies in T2DM cases were significantly different from the control population. We found a significant association of KCNJ11 (rs5210) gene polymorphism with T2DM in North Indian patients indicating the role of this variant in developing risk for T2DM.

Introduction: Type 2 diabetes (T2D) is a major driver of health care costs, thus treatments enabling T2D reversal may reduce expenditures. We examined the impact of a T2D continuous care intervention (CCI) on health care utilization. Previous research documented that CCI, including individualized nutrition supported by remote care, simultaneously reduced hemoglobin A1c and medication use and improved cardiovascular status after two years; however, the impact on utilization is unknown. Methods: This study used four years of data (two years pre-intervention, two years post-intervention) from the Indiana Network for Patient Care (INPC) health record. Two methods estimated the impact of CCI on utilization. First, an interrupted time series (ITS) including only CCI participants (n=193) compared post-intervention utilization to expected utilization had the pre-intervention trend persisted. Deviation from the trend was estimated non-parametrically for each 6-month interval after the implementation of CCI . Second, a 1:3 matched comparator group (n=579) was constructed and used for a difference-in-differences (DiD) analysis. The primary outcome was annualized outpatient encounters. Secondary outcomes included emergency encounters and hospitalizations. Results: In two years prior to intervention, CCI participants had a mean of 5.77 annualized encounters (5.62 outpatient, 0.04 hospitalizations, 0.11 emergency). The CCI group showed a reduction in outpatient utilization after intervention. In ITS analysis, 1.6 to 1.9 fewer annualized outpatient encounters occurred in each 6-month interval post-intervention relative to expected utilization based on pre-intervention trends (p<0.01 each 6-month period; 28-33% reduction). The DiD analysis suggested a larger reduction; 5 fewer annualized outpatient encounters in the quarter after intervention, diminishing to 2.5 fewer after 2 years (p<0.01 each quarter). The study was underpowered to draw conclusions about hospitalization and emergency encounters due to the limited number of CCI patients and the rarity of encounters. Conclusions: Outpatient encounters were significantly reduced for a T2D patient population up to 2 years after receiving an individualized intervention supporting nutrition and behavior change through remote care.

Background: Maternal diabetes mellitus (MDM) is associated with increased risks for adverse neonatal outcomes. However, the impact of MDM on neonatal outcomes in Bisha, a city in Saudi Arabia, is not well-documented. This study aims to investigate the impact of MDM on neonatal outcomes in the Maternity and Children’s Hospital (MCH), Bisha, Saudi Arabia. Methods: A retrospective cohort study was conducted on 181 pregnant women with diabetes and their neonates diagnosed at Maternity and Children’s Hospital (MCH), Bisha, Saudi Arabia, between October 5, 2020, and November 5, 2022. The primary outcome was a composite of adverse neonatal outcomes, including stillbirth, neonatal death, macrosomia, preterm birth, respiratory distress syndrome, hypoglycemia, and congenital anomalies. Logistic regression analyses were used to adjust for potential confounders. Results: The total sample size was 181. The average age of patients was 34 years (SD=6.45). The majority of the patients were diagnosed with GDM, 147 (81.2%), and pre-GDM, 34 (18.8%). Neonates born to mothers with MDM had a higher risk of adverse neonatal outcomes compared to those born to mothers without MDM (adjusted odds ratio [aOR] = 1.46, 95% confidence interval [CI]: 1.25-1.70). The risks of macrosomia (aOR = 1.74, 95% CI: 1.38-2.19), LBW (aOR = 1.32, 95% CI: 1.06-1.66), and RDS (aOR = 1.57, 95% CI: 1.28-1.93) were significantly higher among neonates born to mothers with MDM. Types of DM were statistically significant with some neonatal outcomes: hypoglycemia (p-value = 0.017), macrosomia (p-value = 0.050), and neonatal death (p-value = 0.017). Conclusion: MDM is associated with an increased risk of adverse neonatal outcomes in Bisha. Early identification and management of MDM may improve neonatal outcomes and reduce the burden of neonatal morbidity and mortality in this population.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

Obesity, type 2 diabetes, and different forms of cancers are among the leading human diseases and highly complex in terms of diagnostic and therapeutic approaches. Diabetes and cancer are among the most frequent and complex diseases and based on epidemiological evidence and study it can be concluded that the patients suffering from diabetes are considered to be significantly at higher risk for a number of cancer types. Both these diseases are among the highly complex and heterogeneous in nature. There are a number of evidences which support the hypothesis that these diseases interlinked and obesity may aggravate the risk(s) of both these diseases type 2 diabetes and different types of cancers. Multi-level unwanted alterations such as (epi-)genetic alterations, changes at the transcriptional level, and altered signaling pathways (receptor, cytoplasmic, and nuclear level) are the major source which promotes a number of complex diseases and such heterogeneous level of complexities are considered as the major barrier in the development of therapeutic. With so many known challenges, it is critical to understand the relationships and the common shared causes between type 2 diabetes and cancer which is difficult to unravel and understand. Furthermore, the real complexity arises during diagnosis from contended corroborations that specific drug(s) (individually or in combination) during diagnosis process of type 2 diabetes may increase or decrease the cancer risk or affect cancer prognosis. In this review article, we have presented the recent and most updated evidences from the studies where the origin, biological background, correlation between them have been presented or proved. Furthermore, we have summarized the methodological challenges and tasks that are frequently encountered. we have also outlined the physiological links between type 2 diabetes and cancers. Finally, we have presented and summarized the outline of the hallmarks for both these diseases diabetes and cancer.

Positive-sense single-stranded RNA (+ssRNA) viruses comprise many (re-)emerging human pathogens that pose a public health problem. Our innate immune system and in particular the interferon response form the important first line of defense against these viruses. Given their genetic flexibility, these viruses have therefore developed multiple strategies to evade the innate immune response in order to optimize their replication capacity. Already many molecular mechanisms of innate immune evasion by +ssRNA viruses have been identified. However, research addressing the effect of host innate immune evasion on the pathology caused by the viral infection is less prevalent in literature, though very relevant and interesting. Since interferons have been implicated in inflammatory diseases and immunopathology in addition to their protective role in infection, the influence of antagonizing the immune response may have an ambiguous effect on the clinical outcome of the viral disease. Therefore, this review discusses what is currently known about the role of interferons and host immune evasion in the pathogenesis of emerging viruses belonging to the coronaviruses, alphaviruses and flaviviruses.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Type 2 diabetes (T2D) is a chronic systemic disease with a complex etiology, characterized by insulin resistance and mitochondrial dysfunction in various cell tissues. To explore this relationship, we conducted a secondary analysis of complete mtDNA sequences from 1,261 T2D patients and 1,105 control individuals. Our findings revealed significant associations between certain single nucleotide polymorphisms (SNPs) and T2D. Notably, the variants m.1438A>G (controls: 32 [27.6%], T2D: 84 [72.4%]; OR: 2.46; 95%CI: 1.64-3.78; p<0.001), m.14766C>T (controls: 498 [36.9%], T2D: 853 [63.1%]; OR: 2.57, 95%CI: 2.18-3.04, p<0.001), and m.16519T>C (controls: 363 [43.4%], T2D: 474 [56.6%]; OR: 1.24, 95%CI: 1.05-1.47, p=0.012) were significantly associated with diabetes probability. The variant m.16189T>C Previously reported in multiple studies in different populations, it was not found to be associated with T2D in our analysis (controls: 148 [13.39] T2D: 171 [13.56%]; OR: 1.03; 95%CI: 0.815-1.31,; p=0.83). These results provide evidence suggesting a link between some mtDNA polymorphisms and T2D, probably related to association rules and topological patterns and three-dimensional confirmation associated to regions where the changes are, rather than to point mutations in the sequence.

Osteoporosis is a common metabolic bone disease in patients with diabetes, which can develop simultane-ously with Type 2 diabetes (T2D) in postmenopausal women. Bisphosphonate (BP) is administered to pa-tients with both the conditions and may cause medication-related osteonecrosis of the jaws (MRONJ). It affects the differentiation and function of osteoclasts as well as thickness of cortical bone through bone mineralization. Therefore, this study aimed to investigate the effects of T2D on osteoclast differentiation and activity as well as cortical bone formation in postmenopausal patients with MRONJ. Tissue samples were collected from 10 patients diagnosed with T2D and Stage III MRONJ in the experimental group and from 10 patients without T2D in the control group. Histological examination was conducted, and expres-sion of dendritic cell-specific transmembrane protein (DC-STAMP) and tartrate resistant acid phosphatase (TRAP) was assessed. Cortical bone formation was analyzed using CBCT images. The number of TRAP-positive osteoclasts and DC-STAMP-positive mononuclear cells were significantly less in the experi-mental group (p < 0.05). Furthermore, the thickness and ratio of cortical bone were significantly greater in the experimental group (p < 0.05). In conclusion, T2D decreased the differentiation and function of osteo-clasts, and increased cortical bone formation in postmenopausal patients with MRONJ.

In this work, we report the carbon fiber-based wire-type asymmetric supercapacitors (ASCs). The highly conductive carbon fibers were prepared by the carbonized and graphitized process using the polyimide (PI) as a carbon fiber precursor. To assemble the ASC device, the CoMnO2-coated and Fe2O3-coated carbon fibers were used as the cathode and the anode materials, respectively. FE-SEM analysis confirmed that the CoMnO2-coated carbon fiber electrode exhibited the porous hierarchical interconnected nanosheet structures, depending on the added amounts of ammonium persulfate (APS) as an oxidizing agent, and Fe2O3-coated carbon fiber electrode showed a uniform distribution of porous Fe2O3 nanorods over the surface of carbon fibers. The nanostructured CoMnO2 were directly deposited onto carbon fibers by a chemical oxidation route without high temperature treatments. In particular, the electrochemical properties of the CoMnO2-coated carbon fiber with the concentration of 6 mmol APS presented the enhanced electrochemical activity, probably due to its porous morphologies and good conductivity. Further, to reduce the interfacial contact resistance as well as improve the adhesion between transition metal nanostructures and carbon fibers, the carbon fibers were pre-coated with the Ni layer as a seed layer using an electrochemical deposition method. The fabricated ASC device delivered a specific capacitance of 221 F g-1 at 0.7 A g-1 and good rate capability of 34.8% at 4.9 A g-1. Moreover, the wire-type device displayed the superior energy density of 60.16 Wh kg-1 at a power density of 490 W kg-1 and excellent capacitance retention of 95% up to 3,000 charge/discharge cycles.

Diabetes is a risk factor for mild cognitive impairment (MCI) and dementia. However, how the clinical characteristics of type 2 diabetic patients with MCI are linked to sarcopenia and/or its criterion remain to be elucidated. Japanese patients with type 2 diabetes mellitus were categorized into the MCI group for MoCA-J (the Japanese version of the Montreal cognitive assessment) score <26, and into the non-MCI group for MoCA-J ≥26. Sarcopenia was defined by a low skeletal mass index along with low muscle strength (handgrip strength) or low physical performance (walking speed <1.0 m/s). Univariate and multivariate-adjusted odds ratio models were used to determine the independent contributors for MoCA-J <26. Among 438 participants, 221 (50.5%) and 217 (49.5%) comprised the non-MCI and MCI groups, respectively. In the MCI group, age (61 ± 12 vs. 71 ± 10 years, p < 0.01) and duration of diabetes (14 ± 9 vs. 17 ± 9 years, p < 0.01) were higher than those in the non-MCI group. Patients in the MCI group exhibited lower hand grip strength, walking speed, and skeletal mass index, but higher prevalence of sarcopenia. Only walking speed (rather than muscle loss or muscle weakness) was found to be an independent determinant of MCI after adjusting for multiple factors, such as age, gender, BMI, duration of diabetes, hypertension, dyslipidemia, smoking, drinking, eGFR, HbA1c, and history of coronary heart diseases and stroke. In subgroup analysis, a group consisting of male patients aged ≥65 years, with BMI <25, showed a significant OR for walking speed. This is the first study to show that slow walking speed is a sole determinant for the presence of MCI in patients with type 2 diabetes. It was suggested that walking speed is an important factor in the prediction and prevention of MCI development in patients with diabetes mellitus.

Researches on flexible thermoelectric (TE) materials usually focus on conducting polymers (CPs) and CP-based composites; however, it is a great challenge to obtain high TE properties comparable to inorganic counterparts. Here, we report an n-type Ag₂Se film on flexible nylon membrane with an ultrahigh power factor ~987.4 ± 104.1 μWm⁻¹K⁻² at 300 K and an excellent flexibility (93% of the original electrical conductivity retention after 1000 bending cycles around a 8-mm diameter rod). The flexibility is attributed to a synergetic effect of the nylon membrane and the Ag₂Se film intertwined with numerous high-aspect-ratio Ag₂Se grains. A TE prototype composed of 4-leg of the hybrid film generates a voltage and a maximum power of 19 mV and 460 nW, respectively, at a temperature difference of 30 K. This work opens opportunities of searching for high performance TE film for flexible TE devices.

In order to understand the effect of Pb-CuI co-doping on the thermoelectric performance of Bi₂Te₃, n-type Bi₂Te₃ co-doped with x at% CuI and 1/2x at% Pb (x = 0, 0.01, 0.03, 0.05, 0.07, and 0.10) were prepared via high temperature solid state reaction and consolidated using spark plasma sintering. Electron and thermal transport properties, i.e., electrical conductivity, carrier concentration, Hall mobility, Seebeck coefficient, and thermal conductivity, of CuI-Pb co-doped Bi₂Te₃ were measured in the temperature range from 300 K to 523 K and compared to corresponding x% of CuI-doped Bi₂Te₃ and undoped Bi₂Te₃. The addition of a small amount of Pb significantly decreased the carrier concentration, which could be attributed to the holes from Pb atoms, thus the CuI-Pb co-doped samples show a lower electrical conductivity and a higher Seebeck coefficient compared to CuI-doped samples with similar x values. The incorporation of Pb into CuI-doped Bi₂Te₃ rarely changed the power factor because of the trade-off relationship between the electrical conductivity and the Seebeck coefficient. The total thermal conductivity(κ_tot) of co-doped samples (κ_tot ~1.4 W/m∙K at 300 K) is slightly lower than that of 1% CuI-doped Bi₂Te₃ (κ_tot~1.5 W/m∙K at 300 K) and undoped Bi₂Te₃ (κ_tot ~1.6 W/m∙K at 300 K) due to the alloy scattering. The 1% CuI-Pb co-doped Bi₂Te₃ sample shows the highest ZT value of 0.96 at 370 K. All data on electrical and thermal transport properties suggest that the thermoelectric properties of Bi₂Te₃ and its operating temperature can be controlled by co-doping.

Aims/Hypothesis): Type 1 diabetes is an immune-mediated disease with destruction of the pancreatic β-cells, a process that is conditioned by multiple genes and other factors. HLA counts as the major susceptibility gene. Significant variations in HLA genetic susceptibility to type 1 diabetes between Caucasians, African and Asian and other ethnic groups may have led to the variation in incidence of type 1 diabetes globally. Type 1 diabetes is characterized upon HLA identification. In this chapter we discuss global variations in genetic susceptibility of HLA with regard to type 1 diabetes globally with a particular attention to Arab population. Methods): Haplotype configuration of HLA class I A, B, C and Class II –DR/DQ/DP were studied in Caucasians, African and Asian and in Arab population to see if that is responsible for the exponential rise in the rate of type 1 diabetes. Results): Although Arabs have one of the highest global incidence and prevalence rates of type 1 diabetes, unfortunately, there is a dearth amount of information regarding HLA genetic susceptibility to type 1 diabetes in the Arab world. HLA haplotype configurations contribute to its risk value. However, out of an insufficient present study there are examples of misjudgment of HLA risk according to HLA alleles rather than haplotypes. Conclusion): To date HLA outlooks for the characterization of type 1 diabetes. There is an ethnicity difference in HLA characteristics which is responsible for variation in type 1 diabetes. Although Arab population have contributed heavily in the rise of burden of type 1 diabetes, however, there is significantly a dearth amount of studies on HLA in Arab population. Obviously, any future prediction, prevention or cure of the disease will be based on the HLA genetics. There is a dire need for a systematic screening of HLA for Arab population with type 1 diabetes, identification of Arab HLA-risk values and identify those who are prone to get the disease.

In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.

We address weighted composition operators ψCφ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators.

Detection of PLA2R and THSD7A among primary membranous glomerulonephritis (MGN) patients transformed the diagnosis, treatment monitoring and prognosis. Anti-PLA2R can be detected in 70-90% of primary MGN patients while anti-THSD7A in 2-3% of anti-PLA2R negative primary MGN patients depending on the technique used. Serum and urine samples are less invasive and non-invasive respectively and can detect the presence of anti-PLA2R and anti-THSD7A with higher sensitivity and specificity, significant in patients’ monitoring and prognosis better than exposing patients to frequent biopsy which is an invasive procedure. Different techniques of detection of PLA2R and THSD7A in patients’ urine and sera were reviewed with the aim of providing newer and alternative techniques. We proposed the use of biomarkers (PLA2R and THSD7A) in making the diagnosis, treatment decision and follow up of patients with primary MGN. We also reviewed other prognostic renal biomarkers like retinol binding protein (RBP) and beta-2 microglobulin in order to detect progression of renal damage for early intervention.

This study presents a vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA’s is made of a sandwich hollow structure embedded with the electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable viscosity property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficients, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modelling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from stationary random vibration of thin plates.

Background and Objectives Neurofibromatosis 1 (NF1 MIM # 162200), also known as von Recklinghausen disease, is among the most common autosomal dominantly transmitted disorders characterized mainly by neurocutaneous manifestations such as café au lait spots, intertriginous freckling, various types of neurofibromas (cutaneous neurofibromas or plexiform tumors), neurological manifestations, and bone abnormalities. It occurs with an incidence of 1:3000–1:4000 cases. Cone-rod dystrophies belong to the large group of retinal dystrophies, a highly heterogeneous group of disorders clinically manifested mainly by damage to cone and rod cells and have a broad spectrum of clinical manifestations. Many genes are involved in their etiology, with more than 100 currently identified, including the CRX gene responsible for the autosomal dominant form of cone-rod dystrophy (ad CORD). Materials and Methods: The authors present an intriguing case of a patient diagnosed with Neurofibromatosis type 1 (NF1) as an infant and ocular involvement (myopia and astigmatism onset at age 15), which yielded a surprising molecular testing result. Results: Molecular DNA analysis identified a rare occurrence of two mutational variants, including a pathogenic variant in the NF1 gene, c.3871-2A, and a likely pathogenic variant in the CRX gene c.119G>A. Conclusions: The authors present this case to highlight the surprises offered by molecular testing in a condition where the diagnosis is usually based on clinical criteria, thus providing patients with competent genetic advice.

Alzheimer’s disease (AD) and type 2 diabetes mellitus (T2DM) are comorbidities that result from the sharing of common genes. The molecular background of comorbidities can provide clues for the development of treatment and management strategies. Here, the common genes involved in the development of the two diseases and in memory and cognitive function are reviewed. Network clustering based on protein-protein interaction networks identified tightly connected gene clusters that have an impact on memory and cognition among the comorbidity genes of AD and T2DM. Genes with functional implications were intensively reviewed, and relevant evidence was summarized. Gene information will be useful in the discovery of biomarkers and the identification of therapeutic targets for AD.

(1) Background: Little research is done on the link of diabetic kidney disease (DKD) progression and diabetic gastroenteropathy in type 1 diabetes (T1D). (2) Methods. We performed a cross-sectional study with 100 T1D patients, 27 of them had progressive DKD, defined as estimated glomerular filtration rate (eGFR) decline≥3 ml/min/year or increased albuminuria stage over the mean follow-up time of 5.89±1.73 years. Newly developed score with 17 questions on gastrointestinal (GI) symptoms was used. Faecal calprotectin was measured by ELISA. Lower GI endoscopies were performed in 21 patients. (3) Results: Gastrointestinal symptom score demonstrated high reliability (Cronbach's α=0.78). Patients with progressive DKD had higher GI symptom scores compared to those with stable DKD (p=0.019). The former group demonstrated more frequent bowel movement disorders (p=0.04). The scores correlated negatively with eGFR (r = -0.335; p = 0.001), positively with albuminuria (r=0.245; p=0.015), Hba1c (r=0.305, p=0.002), diabetes duration (r=0.251, p=0.012). Faecal calprotectin levels did not differ between DKD groups significantly. The most commonly reported histopathological findings of enteric mucosa were infiltration with eosinophils, lymphocytes, plasmacytes, presence of lymphoid follicles and lymphoid aggregates. Conclusion: progression of DKD positively correlated with gastrointestinal symptoms, but more research is needed to clarify the causal relationships of the gut-kidney axis in T1D.

Alexithymia as the inability to describe one's own feelings, is being increasingly researched. According to contemporary psychodynamic theories, negative emotions cannot be adequately named and externalized, but remain trapped in the body. Recent research shows the connection of alexithymia with numerous somatic diseases. Diabetes mellitus type 2 and obesity represent a great challenge in treatment, and the psychological profiles in these diseases are being studied more and more often. Therefore, alexithymia enters the focus of some research as one that could play a significant role namely in these diseases as the factor that makes a difference. The aim of this paper is a review of the literature with the purpose of understanding the current knowledge about the interconnection between alexithymia, obesity and type 2 diabetes mellitus.

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades and the identification of differential glycemic responders can aid tailored treatment for prevention of pre-diabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among partic-ipants with elevated T2DM risk, to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary inter-vention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females, 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distin-guish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.

Background: The number of people with type 2 diabetes is increasing daily, and therefore effective therapy is needed to successfully regulate glycemia and reduce the risk of associated complications. Recently, an oral formulation of the glucagon-like peptide-1 receptor agonist (GLP-1 RA) semaglutide has become available. Therefore, the aim of our study was to compare the effectiveness of the new oral formulation and the existing injectable formulation of semaglutide in terms of glycemic and body weight control in a real-world setting. Patients and methods: This was a single-center retrospective observational study conducted at the Rijeka Clinical Hospital Centre. A total of 106 patients with inadequately controlled type 2 diabetes (HbA1 ≥ 7%) on different oral or basal insulin supported oral therapy were recruited from the diabetes outpatient clinic, and data from electronic medical records were retrospectively collected and analyzed from May 2021 to November 2022. All subjects were GLP-1 RA naive and consequently prescribed 0.5 or 1.0 mg once weekly injectable semaglutide (IS) or 7 mg or 14 mg once daily oral semaglutide (OS) for at least 6 months. Glycated hemoglo-bin (HbA1c), body weight, and body mass index (BMI) were assessed prior to semaglutide administration and after a 6-month follow-up period. The primary endpoint was the change from baseline in HbA1c, and sec-ondary endpoints were the change in body weight and the proportion of participants with a reduction in body weight of ≥ 5% and ≥ 10%, respectively, 6 months after the initiation of semaglutide treatment. Results: At 6-month follow-up, no significant difference was observed between the two formulations in terms of HbA1c reduction (IS -1.1% vs OS -1.4%, p=0.126) and weight loss (IS -6.50 kg vs OS -5.90 kg, p=0.714). Exactly the same proportion of participants in both groups achieved a weight loss of ≥ 5% (56.7%, n=30). A weight loss ≥ 10% was observed in 20.7% (n=11) of participants administered IS and 15.1% (n=8) of participants adminis-tered OS, respectively (p=0.454). Conclusion: In a real-world setting, oral semaglutide as add-on therapy to ongoing antihyperglycemic treatment in patients with inadequately controlled type 2 diabetes who had not previously received GLP-1 RA demonstrated the same effectiveness as injectable semaglutide in terms of gly-cemic control and weight loss after 6 months of treatment.