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.

The Boltzmann-Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is extensive, but for certain systems such as those dictated by long-range interactions, the entropy must be non-extensive. Tsallis entropy possesses non-extensive characteristics, which is parametrized by a variable q (q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains but a phenomenological tool. To this date very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from micro-physics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in quasi equilibrium state with electrostatic turbulence known as the quasi-thermal noise, it is shown that the value corresponding to q = 9/13 = 0.6923 may be deduced. This prediction is verified against observation made by spacecraft, and it is shown to be in excellent agreement.

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.

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.

We describe a new approach for integrating multiple views of data into a common latent space using non-negative tensor factorization (NTF). This approach, which we refer to as the "Integrated Sources Model" (ISM), consists of two main steps: embedding and analysis. In the embedding step, each view is transformed into a matrix with common non-negative components. In the analysis step, the transformed views are combined into a tensor and decomposed using NTF. Noteworthy, ISM can be extended to process multi-view data sets with missing views. We illustrate the new approach using two examples: the UCI digit dataset and a public cell type gene signatures dataset, to show that multi-view clustering of digits or marker genes by their respective cell type is better achieved with ISM than with other latent space approaches. We also show how the non-negativity and sparsity of the ISM model components enable straightforward interpretations, in contrast to latent factors of mixed signs. Finally, we present potential applications to single-cell multi-omics and spatial mapping, including spatial imaging and spatial transcriptomics, and computational biology, which are currently under evaluation. ISM relies on state-of-the-art algorithms invoked via a simple workflow implemented in a Jupyter Python notebook.

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.

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.

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.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

QSO B0218+357 is a blazar located at a cosmological redshift of 0.944. The source is gravitationally lensed by a spiral galaxy located at the redshift of 0.68. Strong gravitational lensing splits the signals emitted by the source into two components separated by 10-12 days, as observed in radio and gamma-ray bands. In July 2014 a GeV flare was observed by Fermi-LAT, triggering follow-up observations with the MAGIC telescopes at energies above 100 GeV. The expected time delay between the components allowed us to plan broad band MWL observations before, during and after the trailing component of the emission. The MAGIC observations at the expected time of arrival of the trailing component resulted in the first detection of QSO B0218+357 in Very-High-Energy (VHE, >100 GeV) gamma rays. It is both the farthest known VHE object and one of only a few Flat Spectrum Radio Quasars detected in this energy range. We report here the observed multiwavelength spectral and temporal properties of the emission during the 2014 flare.

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.

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

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.

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.

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.

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.

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.

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 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.

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.

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 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.

Reporting on CSR activities has become the essence of reporting for modern business entities. In this regard, particular attention is paid to public interest companies. Therefore, the following paper aims to answer the question of whether there are differences in the linguistic structure of the studied CSR reports in three selected industry indices on the Warsaw Stock Exchange (WSE) in Poland, i.e. WIG-energy index, WIG-fuel index, WIG-mining index and their relationship with the performance of selected companies. The study was conducted on a purposely selected sample of companies between 2013 and 2018. A total of 138 CSR reports and 138 annual separate financial statements prepared in accordance with international balance sheet law were collected. The study was carried out based on a panel regression model. It was found that CSR reports contained similar average percentages of parts of speech such as nouns and adjectives. When linking the economic performance of companies, expressed with selected indices, to the information on the implementation of CSR concepts, it was revealed that the results are more likely to describe business performance when it is satisfactory.

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.

In a single-center, retrospective study, 22 cases were enrolled and divided into two groups: those who underwent surgical wide excision (group A) and those who did not (group B). The study included 13 cases in group A and 9 cases in group B. In group A, 6 cases solely underwent surgical wide excision, while 7 cases received additional treatments like radiotherapy or chemotherapy. Conversely, in group B, 4 cases received chemotherapy, 4 cases received radiotherapy, and 1 case was managed through observation alone. The mean follow-up time was 60.15 months in group A and 43.44 months in group B, with no significant difference observed. In group A, 9 cases resulted in mortality, whereas 6 cases died within the follow-up period in group B. Lesion-free intervals post-operation were observed predominantly in group A, while 7 cases in group B never experienced freedom from skin lesions. Kaplan-Meier survival curve analysis demonstrated a significant difference between the survival curves of the two groups (P = 0.046). Among non-HIV Kaposi’s sarcoma patients, surgical wide excision appears to have a role in treatment. Patients in group A exhibit a more favorable outcome in the survival curve analysis.

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.

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

For the treatment of cancer and other diseases, therapeutic targeting of non-coding RNAs (ncRNAs) such as microRNAs (miRNAs) and long non-coding RNAs (lncRNAs) is an attractive approach. RNA-based therapeutics have been extensively researched over the past decade, with antisense oligonucleotides and small interfering RNAs being the most commonly used. Some of these have even gained FDA approval. However, the results of trials have been mixed, with some studies reporting strong effects while others have shown limited effectiveness or toxicity. Alternative treatments, such as antimiRNAs, are currently in clinical trials. There is growing interest in the use of lncRNA-based therapies. This Perspective discusses the main challenges of ncRNA therapeutics, including specificity, delivery and tolerability. It also highlights emerging approaches that aim to improve their success.

Non-compliant (NC) structures are often encountered in building construction in developing countries. This is a condition whereby erected buildings do not follow regulatory standards, especially in the provision of reinforcements. Therefore, under an earthquake load, the structures do not have sufficient resistance against such load. The structural elements of the building, which often have NC conditions, are the beam-column joints because they do not contain adequate shear reinforcements due to installation difficulty. This study aims to determine the structural performance of the reinforced concrete (RC) frame, which has a reinforcement deficiency in the beam-column joints. Numerical simulation was conducted on the Kakaletsis structure model by modifying the reinforcement details at the joints to represent the NC conditions. The non-linear modeling and analysis of the structural model were carried out using ATENA software. The analysis showed that the reduction in shear reinforcements in the NC model joint caused a decrease in load-carrying capacity by about 26.04%. A shift was also observed in the collapse pattern, i.e., from the beam to the end of the column, causing global failure and reducing the undamaged but increasing more severely damaged condition. This showed that the NC structure, due to the non-conformance of reinforcement, significantly reduced the structure's performance.

An exhaustive list of thirteen instances of reports confirming experimentally the relativistic Doppler relation, are examined. For those involving longitudinal Doppler, the non-relativistic relation is seen to be confirmed, within the reported experimental accuracies, to the same degree as the standard relativistic relation. Higher values of the speed of the emitter would be required to examine further the claimed confirmations. For those reports involving saturation spectroscopy, there is much confusion over the appropriate Doppler relation to be used, together with some serious analytical flaws. For the two cases that involve transverse Doppler, there are seen to be either serious faults in the theoretical part, or intrusion from the first order effect. Therefore, the reported conclusions - that the results for the experiments confirm the relativistic SR relation - cannot be justified by any of the experimental works.

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

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

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

Nonionizing millimeter-waves (MMW) interact with cells in a variety of ways. Here the inhibited cell division effect was investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm2 safety standards. Irradiation using a power density of about 1.0 mW/cm2 , SAR over 5-6 hours on 50 cells/μl samples of Saccharomyces cerevisiae model organism resulted in 62% growth rate reduction compared to the control (sham). The effect was specific for 85-105 GHz range, and was energy and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deleted cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause permanent genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm2) and compared to that of a compact waveguide (17.17 mW/cm2) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. We have shown that non-thermal MMW radiation has potential for future use in treatment of yeast related diseases and other targeted biomedical outcomes.

Nonionizing millimeter-waves (MMW) are reported to interact with cells in a variety of ways. Possible mechanisms of the inhibited cell division effect were investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm² safety standards. ~1.0 mW/cm² exposure over 5-6 hours treatment on 50 cells/μl samples of Saccharomyces cerevisiae model organism, resulted in 62% growth rate reduction compared to control (sham). The effect was specific for 85-105 GHz range and energy dose and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deletion cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm²) and compared to that of a compact waveguide (17.17 mW/cm²) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. Combinations of MMW mediated Structure Resonant Energy Transfer (SRET), membrane modulations eliciting signaling effects, and energetic resonance with biomolecules were indicated to be responsible for the observations reported. Our results provide novel mechanistic insights enabling innovative applications of nonionizing radiation procedures for eliciting targeted biomedical outcomes.

This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two architectures (unrolling the loop) were developed and analyzed. The algorithm recovers sources located at the boundary separating two homogeneous media that make up a two-dimensional non-homogeneous region from measurements on the boundary of such region. The problem of recovering these sources is an ill-posed inverse problem as small errors in the measurement can produce important changes in the source location. Inverse source problems have many applications in different areas, such as engineering and medicine, making the proposed implementation important. The first architecture (mode one) allows considering different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (mode two) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems such as inverse electrocardiography or electroencephalography. The architectures were tested on four FPGAs of the 7 Series of Xilinx: Spartan-7 xc7s100fgga484, Virtex-7 xc7v585tffg1157, Kintex-7 xc7k70tfbg484, and Artix-7 xc7a35tcpg236. The two FPGA implementations of the algorithm were validated using synthetic examples implemented in MATLAB. The results presented here can be extended to concentric spheres and complex geometries.

The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature

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

Wine is a processed beverage that offers high nutritional and health benefits. It is produced from grape must, which undergoes fermentation by yeasts (and sometimes lactic acid bacteria) to create a product that is highly appreciated by consumers worldwide. However, if only one type of yeast, specifically Saccharomyces cerevisiae, were used in the fermentation process, the resulting wine would lack aroma and flavor and may be rejected by consumers. To produce wine with a desirable taste and aroma, non-Saccharomyces yeasts are necessary. These yeasts contribute volatile aromatic compounds that significantly impact the wine’s final taste. They promote the release of primary aromatic compounds through a sequential hydrolysis mechanism involving several glycosidases unique to these yeasts. This review will discuss the unique characteristics of these yeasts (Schizosaccharomyces pombe, Pichia kluyveri, Torulaspora delbrueckii, Wickerhamomyces anomalus, Metschnikowia pulcherrima, Hanseniaspora vineae, Lachancea thermotolerans, Candida stellata, and others) and their impact on wine fermentations and co-fermentations. Their existence and the metabolites they produce enhance the complexity of wine flavor, resulting in a more enjoyable drinking experience.

Post-quantum public cryptosystems introduced so far do not define an scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based in Lizama’s non-invertible Key Exchange Protocol which can be used to implement a public key infrastructure (PKI), secure, scalable, interoperable and efficient. We show functionality of certificates across different certification domains. Finally, we discuss that non-invertible certificates can exhibit Perfect Forward Secrecy (PFS).

It is well established in literature that the public debt and economic growth bear positive and non-linear relationship. However, in recent literature, evidence of no causal relationship is found when accounted for endogeneity in case of advanced economies (Panizza & Presbitero, 2014). Chudik, Mohaddes, Pesaran, & Raissi, (2017) analyse the data on forty countries and find no evidence of universally applicable threshold effect in the relationship between debt and growth. These advancements in the debt-growth literature provides the motivation to re-explore the relationship between public debt and economic growth under non-linearity and endogeneity in context of developing economies of South Asia including Pakistan, India, Bangladesh and Sri-Lanka for the period 1980-2014. There exists a significant, positive but nonlinear relationship between the public debt and economic growth for the selected set of developing countries when accounted for endogeneity and non-linearity. The negative association between the public debt and economic growth for SAARC region is found when the debt level is higher than 61% of GDP which is quite lower than developed economies (90% of GDP). Individual threshold levels for debt-to-GDP ratio divulge that Sri Lanka, Pakistan and India need to control their public borrowings as their current debt levels are higher and/or around the respective threshold levels.

We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

Non-alcoholic steatohepatitis (NASH), which is the most severe manifestation of non-alcoholic fatty liver disease (NAFLD), has been recognized as a major hepatocellular carcinoma (HCC) catalyst. However, the molecular mechanism of NAFLD-NASH-HCC sequence remains unclear and a specific and effective treatment for NASH has not yet been established. The progress in this field depends on the availability of reliable preclinical models which show the steady progress to NASH, liver cirrhosis, and HCC. However, most of NASH mouse models that have been described to date develop NASH generally for more than 24 weeks and there is an uncertainty of HCC development. To overcome such shortcomings of experimental NASH studies, we established a novel NASH-HCC mouse model with very high reproducibility, generality, and convenience. We treated male C57BL/6J mice with a newly developed choline-deficient and methionine-restricted high-fat diet (CDMRHFD) for 60 weeks. Treatment of CDMRHFD for 3 weeks revealed marked steatosis, lobular inflammation, and fibrosis, histologically diagnosed as NASH. Liver cirrhosis was observed in all mice with 36-week treatment. Liver nodule emerged at 12 weeks of the treatment, and diameter >2 mm liver tumors developed in all mice at 24 weeks of the treatment. In conclusion, our rapidly progressive and highly reproducible NASH-liver cirrhosis-HCC model is helpful for preclinical development and research on the pathogenesis of human NAFLD-NASH-HCC. Our mouse model would be useful for the development of novel chemistry for NASH-HCC-targeted therapies or HCC prevention strategies.

This paper presents a study to accurately evaluate defects in reinforced concrete decks using ultrasonic pulse-echo signals. Two validation specimens were designed and tested where reinforced concrete deck slab specimens included planned voids and defects. A commercial Ultrasonic Pulse-Echo (UPE) device obtains 2-D images of the void/defect locations of the reinforced concrete deck. The UPE is based on the ultrasonic shear-wave test method using dry-point-contact transmitting and receiving transducers and employing a synthetic aperture focusing technique. The authors analyzed the recorded UPE A-scan data to enhance the accuracy of estimating the defects' locations using the synthetic aperture focusing technique imaging method. The analysis benefitted from an advanced denoising approach and defect echo peak extraction based on empirical modal decomposition, Hurst exponent characterization, and Hilbert envelope estimation. While output from conventional UPC devices can only provide qualitative results, the new method provides quantitative information on the anomalies inside the reinforced concrete deck. The developed approach accurately assists with assessing the location and depth of the voids/defects in the reinforced concrete deck slabs.

This article is devoted to the problem of genetically coding of inherited cyclic structures in biological bodies, whose life activity is based on a great inherited set of mutually coordinated cyclic processes. The author puts forward and arguments the idea that the genetic coding system is capable of encoding inherited cyclic processes because it itself is a system of cyclic codes connected with Boolean algebra of logic. In other words, the physiological processes in question are cyclical because they are genetically encoded by cyclic codes. In support of this idea, the author presents a set of his results on the connection of the genetic coding system with cyclic Gray codes, which are one of many known types of cyclic codes. This opens up the possibility of using for modeling inherited cyclic biostructures those algebraic and logical theories and constructions that are associated with Gray codes and have long been used in engineering technologies: Karnaugh maps, Hilbert curve, Hadamard matrices, Walsh functions, dyadic analysis, etc. Additionally, the connections of these constructions with statistical rules of genomic DNAs and binary-genomic numbers are considered.

(1) Background: Although multiple studies have reported on the therapeutic effects of Atezo+Bev for the treatment of NASH-related liver cancer, few studies have focused on its effect on liver reserve. Here, we aimed to compare the changes in hepatic reserve during the Atezo+Bev treatment of NAFLD/NASH-related HCC and of non-NAFLD/non-NASH-related HCC. (2) Methods: We retrospectively compared the changes in ALBI score in 109 patients with NAFLD/NASH or non-NAFLD/non-NASH during 12 weeks of treatment with Atezo+Bev for advanced HCC between September 2019 and January 2022. PSM was performed, and the OS, PFS, and PPS of the two groups were compared. (3)Results: The ALBI after 12 weeks of Atezo+Bev treatment was significantly worse in the NAFLD/NASH group than in the non-NAFLD/non-NASH group. Analysis of the 24 propensity score-matched pairs of cases with NAFLD/NASH or non-NAFLD non-NASH yielded similar results. The prognoses of the two groups were similar with respect to OS and PFS, but the NAFLD/NASH group had a significantly shorter PPS. The 24 matched pairs had similar OS and PFS, but the PPS of the NAFLD/NASH group was shorter. (4)Conclusion: Atezo+Bev treatment may worsen hepatic reserve, and there-fore life expectancy, in patients with NAFLD/NASH-related liver cancer.

This article develops a duality principle and a related convex dual formulation suitable for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a model in non-linear elasticity.

The connection of two phenomena - non-conservative friction forces and dissipation-induced instability can lead to many interesting engineering problems. The paper studies general material-dependent damping influence on dynamical instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on a minimal and complex model of a disc brake. A complex system including material-dependent damping is defined in the commercial finite element software. The finite element model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and a disc damping variations on system stability by complex eigenvalue analysis. Analyzes show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

Near-fault ground motions can cause severe damage to civil structures, including bridges. Safety assessment of these structures for near fault ground motion is usually performed through Non-Linear Dynamic Analyses, while faster methods are often used. IMPAb (Incremental Modal Pushover Analysis for Bridges) permits to investigate the seismic response of a bridge by considering the effects of higher modes, which are often relevant for bridges. In this work, IMPAb is applied to a bridge case study considering near-fault pulse-like ground motion records. The records were analyzed and selected from the European Strong Motion Database and the pulse parameters were evaluated. In the paper results from standard pushover procedures and IMPAb are compared with nonlinear Response-History Analysis (NRHA), considering also the vertical component of the motion, as benchmark solutions and incremental dynamic analysis (IDA). Results from the case study demonstrate that the vertical seismic action has a minor influence on the structural response of the bridge. Therefore IMPAb, which can be applied considering vertical motion, remains very effective conserving the original formulation of the procedure, and can be considered a well performing procedure also for near-fault events.

Abrasive Water Jet Machining (AWJM) is a non-conventional machining process that, unlike other methods, is deemed superior because of its applicability, versatility, and no heat-affected zones in the target material. The main objective of this paper was to develop a cheap, practical model for a low-pressure water jet cutting machine and provide some empirical test data for cutting delicate materials. Proper design calculations were performed and are included for both the water jet machine and the two-axis numerical control. Finite Element Analysis results validate the structural integrity of beams and columns in AWJM. Computational Fluid Dynamic analysis of the nozzle shows good agreement with the theoretical calculations regarding the pressure and velocity of the water-abrasive mixture exiting the nozzle. Modal analysis in ANSYS was done to mitigate potential failure due to resonance induced by vibrations. Limited testing on various thicknesses of polystyrene foam ranging from 1-5 mm thickness and rubber sheet of 1 mm thickness showed that even low pressure of 25-30 bar was sufficient to produce a kerf without any burr. However, extensive testing to report optimized parameters like nozzle transverse speed, standoff distance, abrasive flow rate, etc for working at low-pressure ranges is still a consideration for future investigation.

Postprandial glucose levels between 4 and 7.9 hours (PPG4–7.9h) correlate with mortality from various diseases including hypertension, diabetes, cardiovascular disease, and cancer. This study aimed to assess if predicted PPG4–7.9h could diagnose diabetes. Two groups of participants were involved: Group 1 (4420 participants) had actual PPG4–7.9h, while Group 2 (8422 participants) lacked this measure but had all the diabetes diagnostic measures. Group 1 underwent multiple linear regression to predict PPG4–7.9h using 30 predictors, achieving accuracy within 11.1 mg/dL in 80% of the participants. Group 2 had PPG4–7.9h predicted using this model. Receiver operating characteristic curve analysis showed that predicted PPG4–7.9h could diagnose diabetes with an accuracy of 87.3% in Group 2, with a sensitivity of 75.1% and specificity of 84.1% at the optimal cutoff of 102.5 mg/dL. Simulation on 10,000 random samples from Group 2 revealed that 175 participants may be needed to investigate PPG4–7.9h as a diabetes diagnostic marker with a power of at least 80%. In conclusion, predicted PPG4–7.9h appears to be a promising diagnostic indicator for diabetes. Future studies seeking to ascertain its definitive diagnostic value might require a minimum sample size of 175 participants.

Turbulent dissipation is a central issue in the star and galaxy formation process. Its fundamental property of space-time intermittency, well characterised in incompressible laboratory experiments, remains elusive in cosmic turbulence. Progress requires the combination of state-of-the-art modelling, numerical simulations and observations. The power of such a combination is illustrated here where the statistical method intended to locate extrema of velocity shears in a turbulent field is applied to numerical simulations of compressible magneto-hydrodynamical (MHD) turbulence dedicated to dissipation scales and to a nearby turbulent diffuse molecular cloud. We demonstrate that short-spacing increments of observables can detect strongly dissipative structures. In our simulations, we compute structure functions of various synthetic observables and show that they verify Extended Self-Similarity. This allows to compute their intermittency exponents and we show how they could help constraining some properties of the underlying three-dimensional turbulence. In observations of a turbulent cloud close to the Sun in our Galaxy, a remarkable coherent structure of velocity shear extremum is disclosed . At the location of the largest velocity shear, this coherent structure is found to foster 10 × more carbon monoxide molecules than standard diffuse molecular gas, an enrichment supported by models of non-equilibrium warm chemistry triggered by turbulent dissipation. The power of the combination between modelling and observations is also illustrated by observations of the CH+ cation that provide unique quantitative informations on the kinetic energy trail in the massive, multi-phase and turbulent circum-galactic medium of a galaxy group at redshift z = 2.8.

In this paper is presented the design and syntheis of a dynamic output feedback neural network controller for a non-holonomic mobile robot. First the dynamic model of a non-holonomic mobile robot is presented, in which these constraints are considered for the mathematical derivation of a feasable representation for this kind of robot. Then two control strategies are provided based on kinematic control for this kind of robot. The first control strategy is based on driftless control, this means, that considering that the velocity vector of the mobile robot is orthogonal to its restriction a dynamic output feedback and neural network controller is designed in order that the control action would be zero only when the velocity of the mobile robot is zero. The Lyapunov stability theorem is implemented in order to find a suitable control law. Then another control strategy is designed for trajectory tracking purposes, which similar to the driftless controller, a kinematic control scheme is provided but suitable to implement in more sophisticated hardware. In both control strategy a dynamic control law is provided along with a feedforward neural network controller, so in this way, by the Lyapunov theory the stability and convergence to the origin of the mobile robot position coordinates is ensured. Finally, two numerical experiment are presented in order to validate the theoretical results synthetized in this research study. Discussions and conclusions are provided in order to analyze the results found in this research study.

Non-vertebrate species represent about ~95% of known metazoan (animal) diversity. They remain to this day relatively unexplored genetically, but understanding their genome structure and function is pivotal for expanding our current knowledge of evolution, ecology and biodiversity. Following the continuous improvements and decreasing costs of sequencing technologies, many genome assembly tools have been released, leading to a significant amount of genome projects being completed in recent years. In this review, we examine the current state of genome projects of non-vertebrate animal species. We present an overview of available sequencing technologies, assembly approaches, as well as pre and post-processing steps, genome assembly evaluation methods, and their application to non-vertebrate animal genomes.

Background: Thousands of genetic variants have been associated with hematological traits, though target genes remain unknown at most loci. Also, limited analyses have been conducted in African ancestry and Hispanic/Latino populations; hematological trait associated variants more common in these populations have likely been missed. Methods: To derive gene expression prediction models, we used ancestry-stratified datasets from the Multi-Ethnic Study of Atherosclerosis (MESA, including N=229 African American and N=381 Hispanic/Latino participants, monocytes) and the Depression Genes and Networks study (DGN, N = 922 European ancestry participants, whole blood). We then performed a transcriptome-wide association study (TWAS) for platelet count, hemoglobin, hematocrit, and white blood cell count in African (N = 27,955) and Hispanic/Latino (N = 28,324) ancestry participants. Results: Our results revealed 24 suggestive signals (p < 1×10^(-4)) that were conditionally distinct from known GWAS identified variants and successfully replicated these signals in European ancestry subjects from UK Biobank. We found modestly improved correlation of predicted and measured gene expression in an independent African American cohort (the Genetic Epidemiology Network of Arteriopathy (GENOA) study (N=802), lymphoblastoid cell lines) using the larger DGN reference panel; however, some genes were well predicted using MESA but not DGN. Conclusions: These analyses demonstrate the importance of performing TWAS and other genetic analyses across diverse populations and of balancing sample size and ancestry background matching when selecting a TWAS reference panel.

The quality and shelf-life of NCS (Non-centrifugal sugar) mainly depend on the moisture content present in it. NCS formed by the current practice of open sun drying contains moisture substantially greater than the acceptable level of 3%. This paper presents the work taken up to design a tunnel dryer to attain require moisture content in granular NCS for various load conditions. Initially, an experimental investigation had been carried out on a laboratory scale dryer to achieve required moisture content (< 3%) for various load conditions. This experimental data was used for validating two drying models and found that one of the models is best suitable for designing an industrial-scale dryer. For various load conditions on each tray and dryer exit temperature, nine different cases were arrived at. The number of trucks, trays, drying time and energy requirements were computed using the suitable theoretical model. Tunnel dryer with a length of 18 m, a height of 1.2 m, a width of 1 m, number of trucks of 18 and 24 number of trays on each truck was found to be the suitable dryer to dry 1 tone of NCS based on the minimum energy requirement of 176.49 MJ, and a minimum drying time of 68 minutes.

Untranslated regions (UTRs) of flaviviruses contain a large number of RNA structural elements involved in mediating the viral life cycle, including cyclisation, replication, and encapsidation. Here we report on a comparative genomics approach to characterize evolutionarily conserved RNAs in the 3'UTR of tick-borne, insect-specific and no-known-vector flaviviruses in silico. Our data support the wide distribution of previously experimentally characterized exoribonuclease resistant RNAs xrRNAs within tick-borne and no-known-vector flaviviruses and provide evidence for the existence of a cascade of duplicated RNA structures within insect-specific flaviviruses. On a broader scale, our findings indicate that viral 3'UTRs represent a flexible scaffold for evolution to come up with novel xrRNAs

The aim of the study was to identify factors associated with non-adherence to tuberculosis (TB) preventive treatment among contacts with latent TB infection of new cases of pulmonary TB cases reported in Catalonia in 2019-2021. All contacts aged 18 years or older with a latent TB infection who received a TB preventive treatment were included in the study. The Chi square test and the odds ratios (OR) were used to assess the association between non-adherence to TB preventive treatment and the study variables, considering a p < 0.05 as statistically significant. Multiple logistic regression analysis was used to detect the in-dependent factors associated with TB preventive treatment non-adherence, considering a p < 0.05 as statistically significant. The percentage of non-adherence to TB preventive treatment found in this study was 23.7%. A multivariable logistic regression analysis determined that the following factors were significantly associated with TB preventive treatment non-adherence among adult contacts: “exposure at school or workplace” (aOR = 3.34), “exposure to an index case without laboratory confirmation of TB” (aOR = 2.07), “immigrant contact” (aOR = 1.81), “male gender” (aOR = 1.75) and “exposure duration <6 hours per week or sporadic exposure” (aOR = 1.60). By contrast, the factor “short-term TB preventive treatment regimen” (aOR = 0.38) was significantly associated with a lower treatment non-adherence. Adherence to TB preventive treatment should be improved among adult contacts of TB pulmonary cases with latent TB infection by recommending short-term treatment regimens and by developing health education activities, with a greater focus on contacts with factors associated with treatment non-adherence.

Non-alcoholic beer (NAB) or low alcoholic beer (LAB) are taking over the market with a growing sale. Sus-tainable recycling and valorization of exhausted brewer’s spent grains (BSG) coming from craft beer is a relevant issue in brewing process. In this work, recycled BSG and BSG+GJ (supplemented with 10% grape juice) were used as wort-substrate to inoculate already selected non-conventional yeasts to produce NABLAB craft beer. Results showed that wort composed by only recycled BSG produced appreciate NAB beers (ethanol from 0.12% to 0.54 % v/v) while the addition of 10% of grape juice made LAB beers (ethanol from 0.82 to 1.66 % v/v). As expected, volatile compounds production was highest with the addition of grape juice. Lachancea thermotolerans confirmed the lactic acid production and, as Saccharomyces cerevisiae, is characterized by (in both worts) ethyl butyrate and isoamyl acetate, while Torulaspora delbrueckii produced relevant amounts of exanol, phenylethyl acetate and β-phenyl ethanol (wort added with grape juice). Wickeramhomyces anomalus and Pichia kluyvery showed consistent volatile production but only in wort with grape juice addition where a fermentation activity was exhibited. The overall results indicated that reused BSGs, non-conventional yeasts and grape juice is a suitable strategy for specialty NABLAB beer.

With increased vulnerabilities and vast technology landscapes, it is extremely critical to build systems which are highly resistant to cyber-attacks, to break into systems to exploit. It is almost impossible to build 100% secure authentication & authorization mechanisms merely through standard password / PIN (With all combinations of special characters, numbers & upper/lower case alphabets and by using any of the Graphical password mechanisms). The immense computing capacity and several hacking methods used, make almost every authentication method susceptible to cyber-attacks in one or the other way. Only proven / known system which is not vulnerable in spite of highly sophisticated computing power is, human brain. In this paper, we present a new method of authentication using a combination of computer’s computing ability in combination with human intelligence. In fact this human intelligence is personalized making the overall security method more secure. Text based passwords are easy to be cracked ^[6]. There is an increased need for an alternate and more complex authentication and authorization methods. Some of the Methods ^{[7] [8]} in the category of Graphical passwords could be susceptible, when Shoulder surfing/cameras/spy devices are used.

Previous studies demonstrate the critical importance of non-coding RNAs interfacing with chromatin-modifying machinery resulting in promoter-enhancer-based gene regulation and raise the possibility that many other enhancer-like RNAs may operate via similar mechanisms. Critically, more than 80% of the disease-linked variations identified in genome-wide studies are located in the non-coding regions of genomes, especially non-coding RNA, suggesting non-coding RNAs are relevant to disease. Thus, a critical path forward for understanding non-coding RNAs' role, especially long non-coding RNAs, is to understand the genomic regions' transcriptional regulation, especially non-coding regions. Here, we developed a user-friendly R package called SomaGene for studying and identifying enhancer-like non-coding RNAs with enriched somatic mutations in the cancer genome. SomaGene accepts different genomic variants (whole genome/exome somatic point mutations, structural variations, copy number variations) to identify those RNAs that significantly mutated in diseases (e.g., cancer). It then uses multiple publicly available genomics and epigenetics datasets including ENCODE epigenomics annotations, FANTOM5 tissue-specific expression profiles, disease-associated genome-wide association SNPs, and tissue-specific eQTL pairs to identify those RNAs with potentially enhancer function. SomaGene, as a powerful R package, can provide the opportunity to cancer scientists to study the roles of non-coding RNAs in different cancer genomes.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Numerical models widely used for hydrocarbon phase behavior and compositional flow simulations are based on assumption of thermodynamic equilibrium. However, it is not uncommon for oil and gas-condensate reservoirs to exhibit essentially non-equilibrium phase behavior, e.g., in the processes of secondary recovery after pressure depletion below saturation pressure, or during gas injection, or for condensate evaporation at low pressures. In many cases the ability to match field data with equilibrium model depends on simulation scale. The only method to account for non-equilibrium phase behavior adopted by the majority of flow simulators is the option of limited rate of gas dissolution (condensate evaporation) in black oil models. For compositional simulations no practical yet thermodynamically consistent method has been presented so far except for some upscaling techniques in gas injection problems. Previously reported academic non-equilibrium formulations have a common drawback of doubling the number of flow equations and unknowns compared to the equilibrium formulation. In the paper a unified thermodynamically-consistent formulation for compositional flow simulations with non-equilibrium phase behavior model is presented. Same formulation and a special scale-up technique can be used for upscaling of an equilibrium or non-equilibrium model to a coarse-scale non-equilibrium model. A number of test cases for real oil and gas-condensate mixtures are given. Model implementation specifics in a flow simulator are discussed and illustrated with test simulations. A non-equilibrium constant volume depletion algorithm is presented to simulate condensate recovery at low pressures in gas-condensate reservoirs. Results of satisfactory model matching to field data are reported and discussed.

This study aimed to investigate whether non-fasting plasma triglycerides were associated with diabetes mortality. It included 7,312 US adult participants. Diabetes mortality data were obtained via linkage to the National Death Index (NDI) records. Hazard ratios of non-fasting plasma triglycerides for diabetes mortality were assessed using Cox proportional hazards models, adjusting for age, gender, ethnicity, obesity, poverty-income ratio, education levels, physical activity, alcohol consumption, cigarette smoking status, survey period, hypercholesterolemia, hypertension, diabetes, and family history of diabetes. Among these participants, 1,180 had diabetes. A total of 420 diabetes-caused deaths were recorded during a mean follow-up of 16.8 years. A 1-natural-log-unit increase in non-fasting plasma triglycerides was associated with a 41% higher diabetes mortality risk (hazard ratio, 1.41; 95% confidence interval, 1.19-1.67). Participants with non-fasting plasma triglycerides in the highest quintile, versus those in the lowest quintile, had a 144% higher diabetes mortality risk (hazard ratio, 2.44; 95% confidence interval, 1.49-4.02). The positive association of non-fasting plasma triglycerides with diabetes mortality was independent of diabetes status at the baseline. In conclusion, this study demonstrated that non-fasting plasma triglycerides were positively associated with diabetes mortality, independent of diabetes status at the baseline. Non-fasting triglycerides may be a therapeutic target for diabetes-related complications.

GCTs are developmental tumors and likely to reflect ontogenetic and teratogenetic determinants. The objective was to identify syndromes with or without congenital anomalies and non-syndromic defects as potential risk factors. Patients with extracranial GCTs (eGCTs) registered in MAKEI 96/MAHO 98 between 1996 and 2017 were used. According to Teilum's holistic concept malignant and benign teratomas were registered. We used a case control study design with Orphanet as a reference group for syndromic defects and the Mainz birth registry (EUROCAT) for congenital anomalies at birth. Co-occurring genetic syndromes and/or congenital anomalies were assessed accordingly. Odds ratios and 95% confidence intervals were calculated and p-values for Fisher’s exact test with Bonferroni correction if needed. A strong association was confirmed for Swyer (OR 338.6, 95% CI 43.7-2623.6) and Currarino syndrome (OR 34.2, 95% CI 13.2-88.6). We additionally found 17 isolated cases of eGCT with a wide range of syndromes, however not significantly associated following Bonferroni correction. All these cases pertained to girls. Regarding non-syndromic defects, no association with eGCTs could be identified. In our study we confirmed a strong association for Swyer and Currarino syndromes with additional congenital anomalies.

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

Despite significant milestones in armed conflict research generally and climate security research specifically, methodologically tight explanation of naturally caused armed conflict still leaves much to be desired. In this article we unpack the black box of the climate-security nexus and advance causal modelling of armed conflict. To infer effects of natural causes on armed conflict outcomes, we apply recent advances in causal methods to conflict outcomes that have been non-experimentally observed across Iraqi municipalities. Retrieval of an entire empirical causal structure of climate-conflict pathways allows us to corroborate the existence of a cause-and-effect relationship between climatological, environmental, and demographic variables and armed conflict. We confirm that soil temperature, population density, and variability of latent energy cause an increase in fatalities, while rice production decreases fatalities. We discuss our findings, their limitations, and future research directions, and reflect on their relevance for policy interventions.

Background: Despite scientific advances, the management of procedural pain in neonates remains suboptimal. Applying adequate therapy to control pain during the neonatal period is a moral and ethical act. In recent decades, ample evidence has accumulated regarding the risks, associated with both untreated pain and the use of more aggressive analgesic therapy. Thus, the emphasis in neonatal clinical practice is on non-aggressive pain management techniques, including homeopathic agents. The efficacy and safety of homeopathic agents for reducing procedural pain in neonates is the subject of the present study. Materials and Methods: Healthy full-term newborn babies with an average age of 72-84 hours were included. They were divided into three study groups: group (A) – not anesthetised, /n= 67/, group (B) – anesthetised with Arnica D30 /n=40/ and group (C)- anesthetised with Sol.Glucose 25% /n=40/. The severity of the pain was assessed using the multimodal - Neonatal Infant Pain Scale (NIPS) and the unimodal - Neonatal Facial Coding System (NFCS) scale. Assessments were done 30s before, 30 seconds after, and 5 minutes after the painful stimulus caused by the heel prick. Heart rate, transcutaneous oxygen saturation, respiratory rate and blood pressure were examined at the same intervals. The results obtained were processed statistically by descriptive analysis and ANOVA at a significance level of p&lt; 0.05. Results: 5 minutes after heel prick both scales showed a statistically significant lower score in those given Arnica D30, compared to those who received Sol.Glucose 25%. When monitoring the physiological indicators, we found a significant increase in the heart rate 30 seconds after the procedure.5 minutes after the heel prick we recorded significantly respiratory rate and systolic blood pressure in all three groups compared to pre-procedural values. Conclusions: Arnica D30 has better analgesic effects compared to Sol.Glucose 25% for newborn babies after heel prick tests.

Approximately 300 million non-cardiac surgeries are performed each year. Perioperative mortality after non-cardiac surgery is estimated at 2% in patients over 45 years of age . Half of these deaths are attributable to cardiovascular complications, and most to perioperative myocardial infarction (MINS). Before introduction of cardiac biomarkers the diagnosis of postoperative myocardial infarction was based on symptoms and electrocardiographic changes and its incidence was largely underestimated. The incidence of MINS when standard troponin assay is used ranges between 8 and 19% but increases to 20-30% whit high sensitivity troponin assays. Higher troponin values sugegsting myocardial injury , both with or without definite diagnosis of myocardial infarction, are associated with increased 30 day and 1-year mortality . Diagnostic and therapeutic strategies are reported .

Malnutrition problems are related to diets that lack one or more essential elements, which it is extremely important to food enrichment to improve the content of compounds effective for health. The objective of this study is to evaluate the effect of the addition of Ca2+, K+ and Mg2+ on the induction of nutraceutical quality in grafted tomatoes grown in the NFT (Nutrient Film Technique) system. In the experiment, two factors were evaluated: plants with and without grafting and the foliar application of 10 ml L−1 Ca2+, 4 ml L−1 K+ and 10 ml L−1 Mg2+ cations separately for each case, in addition to the control. The treatments were evaluated using a completely randomized design, with 5 repetitions per treatment. The interactive effects between grafting and foliar application of Ca2+ induced a greater content lycopene, β-carotene and total flavonoids in fruits of tomato. The interactive effects between the graft and the Mg2+ foliar applications obtained the best results in the phenol content. As regards, capacity DPPH and ABTS, the graft decreased concentration, increasing the content of these through foliar applications of calcium. Regarding the enzymatic variables, graft factor increased activity catalase, glutathione peroxidase and phenylalanine ammonium lyase, obtained the best results graft interaction and foliar application of calcium and magnesium. The results obtained demonstrate the influence of the use of grafts and foliar applications of cal-cium and magnesium as tools that could improve the nutraceutical quality content of tomato crop

Metformin is an oral antidiabetic agent with antimicrobial properties, excreted in an active and unmetabolized form. Like some non-antibiotic drugs, subinhibitory concentrations of metformin may contribute to the expression of microbial resistance in wild-type strains. This work aimed to evaluate the biofilm formation of Pseudomonas aeruginosa TGC04 exposed to 100 and 200 µg/mL of metformin, varying the Chemical Oxygen Demand (COD) and flow regime. Biofilms were quantified after 2 and 24 hours, observing reductions and increases in biofilm growth around 13 and 64%, respectively. The greatest biofilm growth occurred in cells exposed to 200 µg/mL of metformin. Both the flow regime and COD concentration were important for the development of the biofilm, whose cells were mostly weakly to moderately adhered. The study provides evidence that in polluted aquatic systems with turbulent regimes, the inhibitory concentration of metformin promoted the least disturbances to the biofilm.

In this review, we will cover a general overview of the current panorama on lncRNAs with an actual or potential role as biological markers in cancer. We will discuss examples of multi-omics approaches that integrates information on somatic aberrations, gene expression and epigenomics, with the scope of providing a more comprehensive view of the functional impact of lncRNA profiles and how these paradigm can be exploited for the discovery and selection of lncRNAs with a functional role and their use as variables informing on progression and prognostic and help guiding the selection of therapeutic strategies for cancers. Finally, we propose a perspective for future evolution of the study of lncRNAs and the discovery of their functional and harnessing their potential to assist in clinical management of malignancies.

Small bowel non-Meckelian diverticulosis is a rare condition with only few published cases despite being described over 200 years ago. In the midst of the COVID-19 pandemic, studies suggested that a lot of patients may experience gastrointestinal manifestations. Intestinal symptoms could worsen the inflammation and infection associated with small bowel diverticulitis. Here, we present two cases: one with inflammation and rupture in a COVID-19 patient and the other as an asymptomatic detection. Furthermore, we provide a mini-review of the literature to emphasize the importance of considering this entity in the differential diagnosis of an acute abdomen.

This publication delves into the intricate world of human communication, extending beyond the realm of spoken and written language to explore the profound influence of non-verbal communication. Focusing on body language—comprising gestures, facial expressions, postures, and movements—it reveals the pivotal role it plays in conveying emotions, intentions, and psychological states. The rapidly evolving fields of neuroscience and cognitive science are investigating the neural mechanisms and cognitive processes that underpin the interpretation and utilization of these non-verbal cues. Notably, the amygdala's involvement in processing emotional facial expressions has provided a neurological foundation for our emotional understanding in non-verbal communication. Concurrently, cognitive psychology sheds light on how perception, attention, and memory influence our interpretation of non-verbal cues and communication strategies.In our modern, technologically advancing society characterized by global interconnectivity and cultural diversity, the significance of non-verbal communication, especially in digital and virtual contexts, is paramount. The transformation of non-verbal expression into digital symbols like emoticons and emojis raises questions regarding its ability to maintain authenticity and emotional understanding. This publication endeavors to comprehensively explore the fundamental role of body language and non-verbal communication in contemporary society. By integrating insights from psychology, neuroscience, social sciences, and digital technologies, it aims to elucidate the underlying mechanisms guiding non-verbal communication. Additionally, it delves into the implications of non-verbal communication across diverse domains, including interpersonal communication, the workplace, politics, advertising, and the virtual world.The research presented herein strives to offer a thorough understanding of interpersonal dynamics, relationships, and social behavior, with the goal of promoting the development of more effective, conscious, and ethically guided communication strategies. Ultimately, this analysis aspires to inspire further interdisciplinary research and reflection, addressing emerging challenges and fully leveraging the potential of non-verbal communication in modern society. This, in turn, guides our path towards a communication landscape that is more inclusive, authentic, and empathetic.

Although adult spontaneous (non-diabetic) hypoglycaemia is rare, its recognition is important for the preventative or curative treatment of the underlying cause. Establishing Whipple’s triad; low blood glucose, neuroglycopaenia and resolution of neuroglycopaenia on increasing blood glucose levels to normal or above, is essential to verify hypoglycaemia. Awareness that hypoglycaemia may occur in severely ill patients is important for its prevention. Further investigation in such cases is unnecessary unless another cause of hypoglycaemia is suspected. Patients are often asymptomatic and normoglycaemic at review. History of medication, self-medication, access to hypoglycaemic drugs, alcohol and comorbidity may provide aetiological clues. The investigation involves obtaining blood samples during symptoms for laboratory glucose measurement or provoking fasting or postprandial hypoglycaemia as directed by symptoms. If confirmed, insulin, c-peptide, proinsulin, beta-hydroxybutyrate are analysed in hypoglycaemic samples. These will classify hypoglycaemia due to non-ketotic hyperinsulinaemia, non-ketotic hypoinsulinaemia and ketotic hypoinsulinaemia and direct investigations to identify the underlying cause. There are, however, many pitfalls, which may mislabel healthy individuals as “hypoglycaemic” or misdiagnose treatable or preventable causes of spontaneous hypoglycaemia. Clinical acumen and appropriate investigations will mostly identify hypoglycaemia and its cause.

This paper presents ConF, a novel deep learning model designed for accurate and efficient prediction of non-coding RNA families. NcRNAs are essential functional RNA molecules involved in various cellular processes, including replication, transcription, and gene expression. Identifying ncRNA families is crucial for comprehensive RNA research, as ncRNAs within the same family often exhibit similar functionalities. Traditional experimental methods for identifying ncRNA fam-ilies are time-consuming and labor-intensive. Computational approaches relying on annotated secondary structure data face limitations in handling complex structures like pseudoknots and have restricted applicability, resulting in suboptimal prediction performance. To overcome these chal-lenges, ConF integrates mainstream techniques such as residual networks with dilated convolutions and cross multi-head attention mechanisms. By employing a combination of dual-layer convolu-tional networks and BiLSTM, ConF effectively captures intricate features embedded within RNA sequences. This feature extraction process leads to significantly improved prediction accuracy compared to existing methods. Experimental evaluations conducted on a ten-fold publicly available dataset demonstrate the superiority of ConF in terms of accuracy, sensitivity, and other perfor-mance metrics. Overall, ConF represents a promising solution for accurate and efficient ncRNA family prediction, addressing the limitations of traditional experimental and computational methods.

Background: Chronic, non-cancer pain represents a serious public health and economic issue affecting approximately 20% of the global population. Chronic pain can affect many aspects of patient’s lives, including mental health, employment, and relationships. Current medical management is largely focussed on investigating and managing acute pain. Patients and clinicians are now increasingly aware of the potential benefits of combined treatments or complex interventions in alleviating chronic pain. These approaches include both physical interventions, such as exercise or yoga, as well as psychological support including cognitive behavioural therapy (CBT) and talking therapies. Methods: This study used network meta-analyses to explore the prevalence of complex interventions in pain management, and the effects of these interventions on quality of life, using outcome measures including intensity of chronic pain, assessment of functional disability and participant’s psychological state. Results: Psychological interventions were associated with improvements in pain intensity and depression. Exercise and manipulation technique-based treatments provided a statistically significant reduction in pain intensity. This effect was enhanced when exercise and CBT were combined. Mensendieck somatocognitive therapy (MSCT) plus standard gynaecological treatment (STGT) treatments appeared to have a better effect on chronic pain than multimodal exercise plus CBT treatment. Combined MSCT and STGT treatment, and multimodal exercise plus CBT treatments, reduced pain intensity, whilst MSCT+STGT treatments had a slightly better effect than exercise plus CBT treatment.Conclusions: Complex interventions have become more popular with patients as the risks associated with other interventions including surgery and pharmacological management have become better understood. These interventions can have a significant positive effect both on the physical and psychological health of patients. The analysis presented in this study suggests that further work is warranted in this area and that additional studies are required, both in more geographically diverse locations, and with larger cohorts.

Fermented food matrices, including beverages, can be defined as the result of the activity of complex microbial ecosystems where different microorganisms interact according to different biotic and abiotic factors. Certainly, in industrial production the technological processes aim to control the fermentation to place safe foods on the market. Therefore, if food safety is the essential prerogative, consumers are increasingly oriented towards a healthy and conscious diet driving the production and consequently the applied research towards natural processes. In this regard, the aim to guarantee safety, quality and diversify of products should be reached limiting or avoiding the addition of antimicrobials or synthetic additives using the biological approach. In this paper, following the recent re-evaluation of non-Saccharomyces yeasts (NSYs) has been re-viewed the bio-protectant and biocontrol activity with a particular focus on their antimicrobial power, probiotic features and promoting functional aspects. In this review, the authors would underline the contribution of NSYs in all food production chain and its role in the technological and fermentative features for their practical and useful use as biocontrol agent in food preparations.

The need to regulate the non-exhaust particulate emissions from vehicles has been discussed worldwide due to the toxicity to the human body as well as the atmosphere. In-depth studies have been conducted on precise analysis of the non-exhaust particulates, in particular, accurate measurement of tire-brake-road wear particles, and their proportion in the atmosphere. In this study, the influence of tire and road wear particles (TRWP) on particulate matter (PM) in the atmosphere was investigated through tire and PM samples. PM samples were collected from the atmosphere using a high-volume sampler equipped with a quartz filter. Additionally, polycyclic aromatic hydrocarbons (PAHs) and heavy metals in tire rubber were analyzed as markers by pyrolysis-gas chromatography/mass spectrometry (GC/MS), GC/MS, and inductively coupled plasma/mass spectrometry (ICP/MS). More vinylcyclohexene was detected than dipentene in the markers measured in the samples of tires equipped with vehicles driving on the road with the high-volume sampler installed, while more dipentene was detected in total suspended particles (TSP) samples. Among the PAHs measured in tire samples, pyrene exhibited the highest concentration. In TSP samples, benzo(b)fluoranthene showed the highest concentration. Among the heavy metals, zinc exhibited the highest concentration in all tire samples and calcium in TSP samples.

With the development of data science, more and more machine learning technologies have been designed to solve complicated and challenging real-world tasks containing a large volume of data. And many significant real-world datasets contain data in the form of networks or graphs. Graph Neural Networks is one of the powerful machine learning tools, which could provide a perfect solution to processing a large amount of non-Euclidean data. And because most bio information data in bioinformatics is in the non-Euclidean domain, Graph Neural Networks could then directly be applied to solve problems in bioinformatics. Much research has been done in the field of GNN, and there are also some surveys related to GNN and its applications. However, there has been little research focusing on GNN in bioinformatics, and we think in the future we could better utilize GNN in the field of biology, so we would like to write a literature review to help take a comprehensive look at GNN and their applications in the field of bioinformatics. In this paper, we would first introduce SOTA models in Graph Neural Networks, and second, introduce their applications in bio information. And then we would provide future directions of Graph Neural Networks in bioinformatics.