The proposed research methodology aims to design a generally implementable framework for providing a house owner/member with the immediate notification of an on-going theft (unauthorized access to their premises). For this purpose, a rigorous analysis of existing systems was undertaken to identify research gaps. The problems found with existing systems were that they can only identify the intruder after the theft, or cannot distinguish between human and non-human objects. Wireless Sensors Networks (WSNs) combined with the use of Internet of Things (IoT), Cognitive Internet of Things, Internet of Medical Things, and Cloud Computing are expanding smart home concepts and solutions, and their applications. The primary objective of the present research work was to design and develop IoT and cloud computing based smart home solutions. In addition, we also propose a novel smart home anti-theft system that can detect an intruder, even if they have partially/fully hidden their face using clothing, leather, fiber, or plastic materials. The proposed system can also detect an intruder in the dark using a CCTV camera without night vision facility. The fundamental idea was to design a cost-effective and efficient system for an individual to be able to detect any kind of theft in real-time and provide instant notification of the theft to the house owner. The system also promises to implement home security with large video data handling in real-time.

Qatar experienced five SARS-CoV-2 waves dominated sequentially by the original virus, Alpha, Beta, Omicron BA.1 and BA.2, and Omicron BA.4 and BA.5, in addition to a prolonged low-incidence phase dominated by the Delta variant. The two-dose primary series of BNT162b2 (Pfizer-BioNTech) COVID-19 vaccine against SARS-CoV-2 infection has been approved for use in 10µg formulations among children and adolescents aged 12-17 years as of May 16, 2021. This study aimed at estimating the effectiveness of the 30µg BNT162b2 Pfizer-BioNTech mRNA COVID-19 vaccine against the pre-Omicron variants of SARS-CoV-2 infection in children and adolescents aged 12-17 years residing in Qatar. A test-negative matched case-control study was conducted where any child or adolescent aged 12-17 years who had been tested for SARS-CoV-2, RT-PCR tests performed on nasopharyngeal or oropharyngeal swabs, as part of contact tracing, between June and November 2021 and eligible to receive the BNT162b2 vaccine as per the national guidelines. Data regarding 14,161 children/adolescents meeting inclusion-exclusion criteria were retrieved from the national Surveillance and Vaccine Electronic System (SAVES). Of the total, 3.1% (444) were positive for SARSCoV-2. More than half (55.96%) were vaccinated with two doses of Pfizer-BioNTech-mRNA COVID-19 vaccine. Amongst those immunized with two doses, 1.2% tested positive for SARS CoV2, while 5.6% amongst the unvaccinated tested positive. The vaccine effectiveness was calculated to be 79%. Pfizer-BioNTech mRNA COVID-19 vaccine provides protection from COVID-19 infection for children/adolescents, hence it is crucial to ensure they receive the recommended vaccines.

Autonomous shuttles have been used as end mile solutions for smart mobility in smart cities. The urban driving conditions of smart cities with many other actors sharing the road and the presence of intersections have posed challenges to the use of autonomous shuttles. Round intersections are more challenging as it is more difficult to perceive the other vehicles in and near the intersection. Thus, this paper focuses on decision making of autonomous vehicles for handling round intersections. The round intersection is introduced first, followed by introductions of the Markov Decision Process (MDP), the Partially Observable Markov Decision Process (POMDP) and the Object Oriented Partially Observable Markov Decision Process (OOPOMDP) which are used for decision making with uncertain knowledge of the motion of the other vehicles. The Partially Observable Monte-Carlo Planning (POMCP) algorithm is used as the solution method and OOPOMDP is applied to decision making for autonomous vehicles in round intersections. Decision making is formulated first as a POMDP problem, and the penalty function is formulated and set accordingly. This is followed by improvement of decision making with policy prediction. Augmented objective state and policy-based state transition are introduced and simulations are used to demonstrate the effectiveness of the proposed method for collision free handling of round intersections by the ego vehicle.

Partially stabilized zirconia (PSZ) is a promising material with superior combination properties in a wide range of industries. In this study, the effect of grain size on the mechanical properties such as hardness, bending strength and fracture toughness (named as ‘indentation toughness’ in this study) was investigated. The multi-doped zirconia ceramics were prepared by powder processing and pressure-less sintered following four sintering schedules. The measured mechanical properties results show that the polymorph structure sintered at a higher temperature has a lower bending strength and hardness. But 300% more indentation toughness (30.54 Kg/mm) of samples sintered at 1600 °C +1150 °C relative to others was estimated due to the grain size effect by our suggested equation. By contrast, the fracture toughness was calculated with an existing method. The results showed that similar trends were obtained. It appeared to be a novel method for evaluating the toughness of partially stabilized zirconia ceramics with micron grains based on the size effect.

Partially automated driving functions (SAE Level 2) can control a vehicle's longitudinal and lateral movements. However, taking over the driving task involves automation risks that the driver must manage. In severe accidents, the driver's ability to avoid a collision must be assessed, considering their expected reaction behavior. The primary goal of this study is to generate essential data on driver reaction behavior in case of malfunctions in partially automated driving functions for use in legal affairs. A simulator study with two scenarios involving 32 subjects was conducted for this purpose. The first scenario investigated driver reactions to system limitations during cornering. The second scenario examined driver responses to phantom braking caused by the AEBS. As a result, the first scenario shows that none of the subjects could control the situation safely. Due to partial automation, we could also identify a new part of the reaction time, the hands-on time, which leads to increased steering reaction times of 1.18 to 1.74 seconds. In the second scenario, we found that 25 of the 32 subjects could not override the phantom braking by pressing the accelerator pedal, although 16 subjects were informed about the system analog to the actual vehicle manuals. Overall, the study suggests that the current legal perspective on vehicle control and the expected driver reaction behavior for accident avoidance should be reconsidered.

Efficient energy extraction in photovoltaic (PV) systems relies on the effective implementation of Maximum Power Point Tracking (MPPT) methods. Conventional MPPT techniques often suffer from slow convergence speeds and suboptimal tracking performance, particularly under dynamic variation of environmental conditions. Smart optimization algorithms (SOA) using metaheuristic optimization algorithms can avoid this limitation inherent in the conventional MPPT methods. The problem of slow convergence of the SOA is avoided in this paper using a novel strategy called Swarm Size Reduction (SSR) utilized with Particle Swarm Optimization (PSO) algorithm, specifically designed to achieve short convergence time (CT) while maintaining exceptional tracking accuracy. The novelty of the proposed MPPT method introduced in this paper is the dynamic reduction of the swarm size of the PSO for improved performance of the MPPT of the PV systems. This adaptive reduction approach allows the algorithm to efficiently explore the solution space of PV systems and rapidly exploit to identify the global maximum power point (GMPP) even under fast fluctuation of uneven solar irradiance and temperature. This pioneering ultra-fast MPPT method represents a significant advancement in PV system efficiency and promotes the wider adoption of solar energy as a reliable and sustainable power source. The novel adaptive PSO algorithm also opens new possibilities for further innovations in optimization-driven applications, extending its potential impact on a diverse range of real-world challenges. The results obtained from this proposed strategy are compared with several optimization algorithms to validate its superiority.

One of the most reliable methods of authentication used today is biometric matching. This authentication process, which is done by using biometrics information such as fingerprint, iris, face, etc. is used in many application areas. Authentication at border gates is one of these areas. However, some restrictions have been introduced to storing and using such data, especially with the General Data Protection Regulation (GDPR). The main goal of this work is to find the practical implementation of fully homomorphic encryption-based biometric matching in border controls. In this paper, we propose a biometric authentication system based on hash expansion and fully homomorphic encryption features, considering these restrictions. One of the most significant drawbacks of the homomorphic encryption method is the long execution time. We solved this problem by executing the matching algorithm in parallel manner. The proposed scheme is implemented as proof-of-concept in the SMILE, and its advantages in privacy preservation has been demonstrated.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

A full electrification of many local railway lines is often not feasible or sustainable in terms of construction and maintenance costs or alternatively for the presence of additional constraints and limitations deriving from environmental or infrastructural limitations. Battery Operated or other kind of hybrid solutions powertrains are currently proposed as sustainable alternatives to Internal combustion engines for the propulsion of rolling stock on not electrified lines. In this work, authors propose the adoption of a partial electrification of lines to assure higher performances and reliability of battery-operated rolling stock designed to be recharged and feed using standard technologies such as pantographs gathering power from suspended catenaries. This innovative solution is designed for a benchmark test vehicle inspired from an existing one and simulated considering some possible scenario of application corresponding to some existing railway lines in Italy.

The security of several full homomorphic encryption (FHE) schemes depends on the hardness of the approximate common divisor (ACD) problem. The analysis of attack and defense against the system is one of the frontiers of cryptography research. In this paper, the performance of existing algorithms, including orthogonal lattice, simultaneous diophantine approximation, multivariate polynomial and sample pre-processing are reviewed and analyzed for solving the ACD problem. Orthogonal lattice (OL) algorithms are divided into two categories (OL-$\land$ and OL-$\vee$) for the first time. And an improved algorithm of OL-$\vee$ is presented to solve the GACD problem. This new algorithm works well in polynomial time if the parameter satisfies certain conditions. Compared with Ding and Tao's OL algorithm, the lattice reduction algorithm is used only once, and when the error vector $\mathbf{r}$ is recovered in Ding et al.'s OL algorithm, the possible difference between the restored and the true value of $p$ is given. It is helpful to expand the scope of OL attacks.

Homogeneous and heterogeneous chemical reactions in partially ionized magneto-nano-liquid are investigated theoretically using finite element method (FEM). The effects of ions and electrons collisions on the transport of heat and mass are analyzed for both the cases of heterogeneous and homogeneous chemical reactions. The simultaneous effects of dispersion of nanosized particles in partially ionized nano-liquid in the presence of magnetic field are also investigated. Through numerical experiments, it is noted that the temperature of partially ionized nano-liquid increases when electrons collision rate and ion collisions are increased. The transport rate of reacting species decreases when heterogeneous and homogeneous chemical reactions strengths are increased. It is also observed that the effect of electron collisions on the flow in y-direction is the same to that of ion collisions on the flow in y-direction. Homogeneous and heterogeneous chemical reactions have similar effects on concentration of chemically reacting species in qualitative sense. However, in quantitative sense, homogeneous chemical reaction has more significant effect on the concentration reacting species as compared to heterogeneous chemical reaction.

The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts on solving the ACD problem as well as its variants were also developed during the past decade. In this paper, an improved orthogonal lattice (OL) based algorithm, AIOL, is proposed to solve the general approximate common divisor (GACD) problem. The conditions for ensuring the feasibility of AIOL are also presented. Compared to the Ding-Tao’s OL algorithm, the well-know LLL reduction is used only once in AIOL, and when the error vector r is recovered in AIOL, the possible difference between the restored and the true value of p is given. The experimental comparisons towards the Ding-Tao’s algorithm and ours are also provided for validating our improvements.

This paper proposes a novel micro-grid structure, which can operate fully-autonomously with inherent seamless switching. It can operate independently in both grid-connected and islanded mode as a self-governed entity without relying on the utility grid. An AC/DC/AC converter is employed as the interface between the micro-grid and the utility grid, which enables the two entities to have different voltages in grid-connected mode. Seamless switching between operation modes can be achieved naturally. The micro-grid is regulated to exchange predefined amount of power with the utility grid in grid-connected mode. This will benefit the power dispatching algorithm of the power system. The predefined power is estimated based on power forecasting of local renewable generations and loads with consideration of the Sate of Charge (SOC) of the battery, and is updated and broadcasted every certain period. A small scale AC micro-grid with a rotating generator, battery storage and solar arrays etc. is built for investigation. Matlab/Simulink results are provided to validate the robustness and flexibility of proposed micro-grid and its operation strategy.

Electric streamer discharges (streamers) in air are a very important stage of lightning, taking place before formation of the leader discharge, and with which an electric discharge starts from conducting objects which enhance the background elecric field, such as airplanes. Despite years of research, it is still not well understood what mechanism determines the values of streamer parameters, such as its radius and propagation velocity. The Streamer Parameter Model (SPM) is aimed to understand this mechanism, as well as to provide a way to efficiently calculate streamer parameters. Previously, we demonstrated that SPM results compared well with a limited set of experimental data. In this Brief Report, we compare SPM predictions to the published hydrodynamic simulation (HDS) results.

The objective of the study was to evaluate the risk factors associated with lower COVID-19 vaccination rates in the United States. The study evaluated the effect of red-blue political affiliation and the effect of the US state's average educational aptitude score and per capita income on states' vaccination rates. The study found that states with concomitantly lower income along with lower educational aptitude scores are less vaccinated while the states with higher income have higher vaccination rates even among those with lower educational aptitude scores. These findings stayed significant after adjusting for red-blue political affiliation where states with red political affiliation have lower vaccination rates. Further study is needed to evaluate how to stop online misinformation among states with low income and low educational aptitude scores; and whether such an effort will increase overall vaccination rates in the United States.

The feasibility of using full ion kinetics, instead of gyrokinetics, in simulating low-frequency Ion-Temperature-Gradient (ITG) instabilities in tokamaks has recently been demonstrated by Sturdevant et al. [Physics of Plasmas 24, 081207 (2017)]. In that work, a variational integrator was developed to integrate the full orbits of ions in toroidal geometry, which proved to be accurate in capturing both the short-time scale cyclotron motion and long time scale drift motion. The present work extends that work in three aspects. First, we implement a relatively simple full orbit integrator, the Boris integrator, and demonstrate that the accuracy of this integrator is also sufficient for simulation of ITG instabilities. Second, the equilibrium magnetic configuration is extended to general toroidal configuration specified numerically, enabling simulation of realistic equilibria reconstructed from tokamak experiments. Third, we extend that work to the nonlinear regime and investigate the nonlinear saturation of ITG instabilities. To verify the new numerical implementation of the orbit integrator and magnetic configuration, the linear electrostatic ITG frequency and growth rate are compared with those given in Sturdevant's work and good agreement is found.

The automatic diagnosis of cardiovascular diseases has received much attention in the deep learning field. In this context, the segmentation of the left ventricle endocardium constitutes a major task in diagnosing heart conditions such as health failure and hypertrophic cardiomyopathy. The objective of this paper is to propose a "deep convolution network" for segmenting the internal cavity of the left ventricle (endocardium) using MRI images. In particular, we design an improved UNET model which handles additional inception modules for efficiently segmenting the internal cavity of the left ventricle. Our approach has been validated on the Sunnybrook Cardiac Data (SCD) dataset and has showed promising results in terms of precision. More specifically, the improved UNET largely outperforms the baseline UNET model and many existing state-of-the-art methods.

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

Macula fovea detection is a crucial prerequisite towards screening and diagnosing macular diseases. Without early detection and proper treatment, any abnormality involving the macula may lead to blindness. However, with the ophthalmologist shortage and time-consuming artificial evaluation, neither accuracy nor effectiveness of the diagnose process could be guaranteed. In this project, we proposed a deep learning approach on ultra-widefield fundus (UWF) images for macula fovea detection. This study collected 2300 ultra-widefield fundus images from Shenzhen Aier Eye Hospital in China. Methods based on U-shape network (Unet) and Fully Convolutional Networks (FCN) are implemented on 1800 (before amplifying process) training fundus images, 400 (before amplifying process) validation images and 100 test images. Three professional ophthalmologists were invited to mark the fovea. A method from the anatomy perspective is investigated. This approach is derived from the spatial relationship between macula fovea and optic disc center in UWF. A set of parameters of this method is set based on the experience of ophthalmologists and verified to be effective. Results are measured by calculating the Euclidean distance between proposed approaches and the accurate grounded standard, which is detected by Ultra-widefield swept-source optical coherence tomograph (UWF-OCT) approach. Through a comparation of proposed methods, we conclude that, deep learning approach of Unet outperformed other methods on macula fovea detection tasks, by which outcomes obtained are comparable to grounded standard method.

The aim of the article is to develop geometrized physics of a vacuum on the basis of two basic postulates: 1) the constancy of the speed of light (more precisely, the speed of propagation of electromagnetic waves) in the vacuum; 2) the ‘vacuum balance condition’ associated with the statement that only mutually opposite formations are born from the vacuum, so that, on average, they completely compensate of the manifestations of each other. The Algebra of signatures is proposed as a mathematical basis for geometrized physics of a vacuum.

Even today, the automatic digitisation of scanned documents in general but especially the automatic optical music recognition (OMR) of historical manuscripts still remain an enormous challenge, since both handwritten musical symbols and text have to be identified. This paper focuses on the Medieval so-called square notation developed in the 11th-12th century, which is already composed of staff lines, staves, clefs, accidentals, and neumes, that are roughly spoken connected single notes. The aim is to develop an algorithm that captures both the neume and pitch, that is melody information that can be used to reconstruct the original writing. Our pipeline is similar to the standard OMR approach and comprises a novel staff line and symbol detection algorithm, based on deep Fully Convolutional Networks (FCN), which perform pixel-based predictions for either staff lines or symbols and their respective types. Then, the staff line detection combines the extracted lines to staves and yields an F1-score of over 99% for both detecting lines and complete staves. For the music symbol detection we choose a novel approach that skips the step to identify neumes and instead directly predicts note components (NCs) and their respective affiliation to a neume. Furthermore, the algorithm detects clefs and accidentals. Our algorithm recognises these symbols with an F1-score of over 96% if the type is ignored and predicts the true symbol sequence of a staff with a diplomatic symbol accuracy rate (dSAR) of about 87%. If only the NCs without their respective connection to a neume, all clefs, and accidentals are of interest the algorithm reaches an harmonic symbol accuracy rate (hSAR) of approximately 90%.

Abstract: Wireless body area networks (WBANs) have strong potential in the field of health monitoring. However, the energy consumption required for accurate monitoring limits the time between battery charges of the wearable sensors, which is a key performance factor (and can be critical in the case of implantable devices). In this paper, we study the inherent trade-off between the power consumption of the sensors and the probability of misclassifying a patient’s health state. We formulate this trade-off as a dynamic problem, in which at each step we can choose to activate a subset of sensors that provide noisy measurements of the patient’s health state. We assume that the (unknown) health state follows a Markov chain, so our problem is formulated as a partially observable Markov decision problem (POMDP). We show that all the past measurements can be summarized as a belief state on the true health state of the patient, which allows tackling the POMDP problem as an MDP on the belief state. We then empirically study the performance of a greedy one-step look-ahead policy compared to the optimal policy obtained by solving the dynamic program. For that purpose, we use an open-source Continuous Glucose Monitoring (CGM) data set of 232 patients over six months and extract the transition matrix and sensor accuracies from the data. We find that the greedy policy saves ~50% of the energy costs while reducing the misclassification costs by less than 2% compared to the most accurate policy possible that always activates all sensors. Our sensitivity analysis reveals that the greedy policy remains nearly optimal across different cost parameters and a varying number of sensors. The results also have practical importance, because while the optimal policy is too complicated, a greedy one-step look-ahead policy can be easily implemented in WBAN systems.

The interpretation of land use and land cover (LULC) is an important issue in the fields of high-resolution remote sensing (RS) image processing and land resource management. Fully training a new or existing convolutional neural network (CNN) architecture for LULC classification requires a large amount of remote sensing images. Thus, fine-tuning a pre-trained CNN for LULC detection is required. To improve the classification accuracy for high resolution remote sensing images, it is necessary to use another feature descriptor and to adopt a classifier for post-processing. A fully connected conditional random fields (FC-CRF), to use the fine-tuned CNN layers, spectral features, and fully connected pairwise potentials, is proposed for image classification of high-resolution remote sensing images. First, an existing CNN model is adopted, and the parameters of CNN are fine-tuned by training datasets. Then, the probabilities of image pixels belong to each class type are calculated. Second, we consider the spectral features and digital surface model (DSM) and combined with a support vector machine (SVM) classifier, the probabilities belong to each LULC class type are determined. Combined with the probabilities achieved by the fine-tuned CNN, new feature descriptors are built. Finally, FC-CRF are introduced to produce the classification results, whereas the unary potentials are achieved by the new feature descriptors and SVM classifier, and the pairwise potentials are achieved by the three-band RS imagery and DSM. Experimental results show that the proposed classification scheme achieves good performance when the total accuracy is about 85%.

The shallow water equations are widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. From a mathematical point of view, they are a hyperbolic system of nonlinear partial differential equations, whose numerical integration is sometimes computationally burdensome. For this reason, the interest of many researchers has been focused on the study of simplified forms of the original set of equations, which requires less computational effort. One of the most commonly applied simplifications consists in neglecting the inertial terms, which changes the hyperbolic model to a parabolic one. The effects of such a choice on the outputs of the simulations of flooding events are controversial and an important topic of debate. In the present paper, two numerical models, recently proposed for the solution of the complete and zero-inertia forms of the shallow waters equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory studies, starting from very simple geometries and moving towards complex topographies. Analyzing the role of the terms in the momentum equations, we try to understand the effect, on the computed results, of neglecting the inertial terms in the zero-inertia formulation. We analyze the computational costs.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

Log collection and storage is a crucial process for enterprises around the globe. Log analysis helps identify potential security breaches and, in some cases, is required by law for compliance. However, enterprises often delegate these responsibilities to third-party Cloud Service Providers (CSPs), where the logs are collected and processed for anomaly detection and stored in a data warehouse for archiving. Prevalent schemes rely on plain (unencrypted) data for anomaly detection. More often, these logs can reveal sensitive information about an organization or the customers of that organization. Hence, it is best to keep it encrypted at all times. This paper presents "SigML++," an extension of work done in "SigML." We utilize Fully Homomorphic Encryption (FHE) with the Cheon-Kim-Kim-Song (CKKS) scheme for supervised log anomaly detection on encrypted data. We use an Artificial Neural Network (ANN) based probabilistic polynomial approximations using a Perceptron with linear activation. We probabilistically approximate the Sigmoid activation function (σ(x)) in the encrypted domain for the intervals [−10,10] and [−50,50]. Experiments show better approximations for Logistic Regression (LR) and Support Vector Machine (SVM) for low-order polynomials.

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

This article is the first part of a scientific project under the general title "Geometrized Vacuum Physics". This study is based on two main postulates: 1) independence of the propagation velocity of electromagnetic waves in vacuum from their frequency; 2) the constancy of the averaged zero vacuum balance, associated with the assertion that only mutually opposite formations are born from vacuum, so that on average they completely compensate for each other's manifestations. In this part of the "Geometrized Vacuum Physics" the foundations of the Algebra of Stignatures are laid, which is the mathematical and logical foundation of the entire project. In the next articles of this project it will be shown that the Algebra of Stignatures can be used for the development of "zero" (vacuum) technologies, algebraic genetics, vacuum cosmology, the vacuum standard model of "elementary particles", vacuum gravity and levitation, vacuum energy, ethics and aesthetics and many other branches of knowledge. At the end of this article, one of the many possible applications of the Algebra of Stignatures is given, in particular, the basics of the stignature-spectral analysis are outlined, with the help of which the possibilities of communication channels can be significantly expanded.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

Transition between the unfolded and native states of the ordered globular proteins is accompanied by accumulation of several intermediates, such as pre-molten globule, wet molten globule, and dry molten globule. Structurally equivalent conformations can serve as native functional states of intrinsically disordered proteins. This overview captures the characteristics and importance of these molten globules in both structured and intrinsically disordered proteins. It also discusses examples of engineered molten globules. The formation of these intermediates under the conditions of macromolecular crowding and their interactions with nanomaterials are also reviewed.