In this paper, it is proved that s-iteration with error and Picard-Mann iteration with error iterative processes converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive map. This convergence is almost -stable and -stable. Applications of these results to the operator equations, where is a strongly accretive and accretive mappings of into itself.

Use of MS Excel as a platform for teaching simple iterative solution of partial differential equations runs into issues of reliability of the computation because of the large number of calculations required. This article documents the problem and an empirical solution. The cause of this unreliability was found by detailed examination of the numerical results from three simultaneous iterations. Computers of several types from different manufacturers were found to fail occasionally in updating variables in the numerical iteration. A simple work-around is suggested and was tested on several platforms.

It has been shown that Human papillomavirus (HPV) infection is associated with several forms of cancer. Additionally, although there are more than 100 types of HPV, more than ten types of it, including types 16 and 18, are considered high-risk. The two proteins that make up the viral capsid of HPV 16 are L1, the major capsid protein, and L2, the minor capsid protein. FDA (The Food and Drug Administration) approved HPV vaccines mostly target L1 and L2 capsid proteins, which facilitate intracellular entry during infection. In this study, it was set out to analyze the creation of phylogenetic relations of L1 nucleic acid sequences of viral isolates. This study also analyzed sequences of three key elements within the amino acid sequences of HPV 16 L1: loops critical for structural stability, nuclear localization signal sequences, and residues implicated in viral attachment. As highlighted by the literature, these elements represent pivotal aspects of viral function. Furthermore, the report highlighted the particular inter-sequence variability within the HPV 16 L1 protein sequences. Overall analysis revealed clustering of sequences primarily due to geographical and characterized by more phylogenetic relatedness within location-specific clusters.

Conditions under which compositions of component systems form a well-defined system-of-systems here are formulated at a fundamental level. Statement of what defines a well-defined composition and sufficient conditions guaranteeing such a result offers insight into exemplars that can be found in special cases such as differential equation and discrete event systems. For any given global state of a composition, two requirements can be stated informally as: 1) the system can leave this state, i.e., there is at least one trajectory defined that starts from the state, and 2) the trajectory evolves over time without getting stuck at a point in time. Considered for every global state, these conditions determine whether the resultant is a well-defined system and if so, whether it is non-deterministic or deterministic. We formulate these questions within the framework of iterative specifications for mathematical system models that are shown to be behaviorally equivalent to the Discrete Event System Specification (DEVS) formalism. This formalization supports definitions and proofs of the afore-mentioned conditions. Implications are drawn at the fundamental level of existence where the emergence of a system from an assemblage of components can be characterized. We focus on systems with feedback coupling where existence and uniqueness of solutions is problematic.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

The properties of iterative splitting methods with serial versions have been analyzed since recent years, see [1] and [3]. We extend the iterative splitting methods to a class of parallel versions, which allow to reduce the computational time and keep the bene t of the higher accuracy with each iterative step. Parallel splitting methods are nowadays important to solve large problems, which can be splitted in subproblems and computed independently with the dierent processors. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, see [2], [10] and [15]. Such a exibilisation with multisplitting methods allow to decompose large iterative splitting methods and recover the bene t of their underlying waveform-relaxation (WR) methods. We discuss the convergence results of the parallel iterative splitting methods, while we could reformulate such an error to a summation of the individual WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods and present dierent numerical applications to validate the bene t of the parallel versions.

Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover’s algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we develop a distributed application with a key-value data structure based on Grover’s algorithm called IQuCS . Consider a database with duplicates. By encoding each element to a binary type with a unique key and forming a key-value pair, we can count the number of occurrences of each element in the database based on quantum computing. We have optimized the operation process by filtering data points to make it more efficient. To determine the effect of this optimization, we evaluate it with datasets of different sizes and with different numbers of duplicates. With the assistance of classical computers, IQuCS can reduce the problem set for each query. Due to this reduction, IQuCS requires fewer qubits. Through the iterative management, IQuCS achieves a reduction of qubit virtualized consumption, up to 66.2%, with reasonable accuracy.

The generation of arithmetic sequences involves arithmetic operations. However, is it possible to generate such sequences without being subject to any arithmetic or related operations, all by just hand? The answer may be negative, as the very rule defining these sequences itself relies on arithmetic operations. Nonetheless, this paper presents a few results demonstrating that the exact sequences of $an$, where, $a \in \{ 2,3,\cdots,9,10\}$ and $n \in \mathbb N \cup \{0\}$, can indeed be generated up to any desired number of terms without relying on any arithmetic operations and others derived from such. This is done by the formation of a specialized table that leverages numerical patterns and the notion of concatenation.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

We present a MATLAB-based, open source reconstruction software for Hybrid Imaging problem arising from Current Density Impedance Imaging (CDII) and Acoustic-Electrical Impedance Tomography (AEIT), utilizing mixed finite element method solver of Darcy toolbox {\tt DarcyLite}~. For a formulation of hybrid inverse problems in impedance tomography the successive substitution iterative schemes are adapted and an reconstruction algorithm is developed. The problem formulation is a class of hybrid imaging modality which is current density impedance imaging or Acoustic-Electrical Impedance Tomography. The proposed algorithm is implemented numerically in two dimensions.

Recombinant laboratory plasmids (RLPs) are common in biological research and freely shared among academic research laboratories (ARLs), a practice required by many research funding agencies. However, the generation of accurate, reproducible results in experiments utilizing RLPs can be hampered by a lack of accompanying sequence information and metadata. This culture of RLP sharing without knowledge of sequence or etiology is accepted by publishers, not regulated by governments, and outside the realm of bio-industry. In addition, no centralized infrastructure currently exists to collate such data, which at the moment is fragmented across companies, non-profits, and governments and thus is not easily accessed or enacted toward threat assessment. The ubiquity, free exchange, and dual-use risk of RLPs exemplifies a biosecurity threat and elevates the need to characterize their composition to facilitate improved biorisk management by the academic community. A number of common sense solutions are available to create a culture that addresses the biosecurity gap posed by RLP sharing. Culture shift in RLP management will require new norms, effective data management for collation of RLP sequences and metadata, and an incentive structure that encourages sequencing by stakeholders. The next generation of researchers must initiate and champion this shift with support from funding agencies and endorsement from governments and international organizations. Coordination of efforts and stakeholders will require international public/private collaboration, a structure that will be critical to ensure widespread utility as well as the ability of lower-resourced partners to participate, contribute, and benefit.

In this letter, we advocate that it is possible to mitigate Pilot Contamination in Massive MIMO systems by scrambling the pilot sequences with a Base Station (BS) scrambling sequence. It is possible if a set of sequences is carefully designed to meet the orthogonality property defined in this letter. Each BS possesses its own scrambling sequence that can be reused the same way frequency reuse is applied to cell deployment. The main advantage of the prosed pilot generation scheme is that the frequency reuse factor can be set to 1, the most aggressive one, while the scrambling sequences can be reused with much less aggressive reuse factors (e.g. 4, 7, 9, 12, etc.), which in consequence results in pilot contamination mitigation and increased system's performance.

We obtain two generalizations of a known theorem of A. Alam and M. Imdad (Fixed Point Theory Appl. 17 (2015) 693–702) showing that some standard proofs can be obtained involving only Cauchy sequences of the successive approximations instead of the usual successive approximations sequences. Suitable examples prove the effective generalization of our results in metric spaces not necessarily complete.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

The demand for explainable and transparent models increases with the continued success of reinforcement learning. In this article, we explore the potential of generating shallow decision trees (DT) as simple and transparent surrogate models for opaque deep reinforcement learning (DRL) agents. We investigate three algorithms for generating training data for axis-parallel and oblique DTs with the help of DRL agents ("oracles") and evaluate these methods on classic control problems from OpenAI Gym. The results show that one of our newly developed algorithms, the iterative training, outperforms traditional sampling algorithms, resulting in well-performing DTs that often even surpass the oracle from which they were trained. Even higher dimensional problems can be solved with surprisingly shallow DTs. We discuss the advantages and disadvantages of different sampling methods and insights into the decision-making process made possible by the transparent nature of DTs. Our work contributes to the development of not only powerful but also explainable RL agents and highlights the potential of DTs as a simple and effective alternative to complex DRL models.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

B chromosomes are supernumerary chromosomes which are found in addition to the normal standard chromosomes (A chromosomes). B chromosomes are well known to accumulate several types of repeats. Although the evolution of B chromosomes has been subject of numerous studies, the mechanisms of accumulation and evolution of repetitive sequences is not fully understood. Recently, new genomic approaches have shed light on the origin and accumulation of different classes of repetitive sequences in the process of B chromosome formation and evolution. Here we discuss the impact of repetitive sequences accumulation on the evolution of plant B chromosomes.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

Original and improved version of the Hardy Cross iterative method with related modifications are today widely used for calculation of fluid flow through conduits in loops-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in the municipalities, water in waterworks or hot water in district heating system, air in the case of ventilation systems in buildings or mines, etc. Since, the resistances in these networks depend of flow, problem is not linear like in electrical circuits, and iterative procedure must be used. In both version of the Hardy Cross method, in original and in the improved one, initial results of calculation in iteration procedure is not flow, but rather the correction of flow. Unfortunately, these corrections should be added to or subtracted from a flow calculated in previous iteration according to complicate algebraic rules. After the here presented node-loop method, final results in each of the iterations is flow directly rather than flow correction. In that way complex algebraic scheme for sign of flow correction is avoided, while the final results still remain unchanged. Numbers of required iterations for the same results are comparable with the improved Hardy Cross method.

Background This paper draws learnings and successes based on field implementation experience spanning four years (2016–2019) of implementing CLTS by Prince of Peace Orphans and Widows Vision, a community-based organization located in Kaberamaido district in eastern Uganda. Methods The study aimed to document, disseminate and inform from an evidence-based point of view how adaptation and collaborative engagements triggers learning from mistakes to inform iterative changes from improvements and success.This is a descriptive paper that used project documents review based on field implementation experience. Existing project reports were synthesised, collated and curated for evidence. Data were drawn from project reports and records to inform narratives in writing. Implementation of the project was executed in homogenous rural communities occupied by people of the same dialect, cultural and social settings. Results We note that success in CLTS implementation can hardly be achieved by merely following prescriptions in handbooks and guidelines but rather by devising innovative community engagement and other participatory and community-driven techniques that foster adaptive management, promote ownership, and buy-in.Having learned from our failures, we used data to inform decisions and transformatively deviated from traditional CLTS implementation and introduced high impact and innovative approaches such as the use of CLTS helpdesks and Situation room, the Pamoja approach, learning labs and iterative feedback loops, innovatively tackling slippage and carefully introducing the follow-up mandona approach. These enhanced experiential learning and ultimately resulted in sustained sanitation behaviour. Conclusions The CLTS approach as outlined in the handbook needs to be flexibly adapted to address contextual needs. Reflective and learning sessions reinforced with routine feedback loops from implementers and beneficiaries yields tremendous results, propagates experiential learning, and ultimately results in a transformative deviation from undesirable to desired sanitation behaviours. These innovative approaches once carefully blended have proved to be sustainable, are adaptable and can work in an even larger scale and in a variety of contexts.

Optical motion capture systems are prone to the errors connected with markers recognition – occlusion, leaving the scene or mislabelling – all these errors are then corrected in the software, but still, the process is not perfect, resulting in artifact distortions. In the article, we examine four existing types of artifacts, then propose the method for detection and classification of the distortions. The algorithm is based on the derivative analysis, low-pass filtering, mathematical morphology and loose predictor. The tests involved multiple simulations using synthetically distorted sequences, comparison of performance to the human operators on real life data and applicability analysis for the distortion removal.

This article addresses the trajectory tracking between two non-identical systems with chaotic properties. We employ the Rossler chaotic and RCL-shunted Josephson junctions model in similar phase space to study trajectory tracking. In order to achieve the goal tracking, we afford two stages to approximate the target tracking. The first stage utilizes the active control technique to transfer the output signal from the RCLs-J system into the quasi-Rossler system. Then next, the RCLs-J system employs the proposed the iterative learning control scheme and the control signal from the drive system to trace the trajectory of Rossler system. The numerical results demonstrate the proposed method and the tracking system is asymptotically stable.

Protein molecules show varying degrees of flexibility throughout their three-dimensional structures. This flexibility is associated with the fluctuation of the torsion angle in proteins. The protein backbone can be defined mainly by two torsion angles, phi (φ) and psi (ψ). The fluctuation of torsion angles is derived from different NMR models’ variations in backbone torsion angles. The angle fluctuations in the cartesian coordinate space are used to characterize the protein’s structural flexibility. Fluctuation of torsion angle is useful in predicting protein function and structure when the torsion angles are used as restraints. This study aims to develop a machine learning method to predict torsion angle fluctuations directly from protein sequences. It explores various useful features such as disorder probability, position-specific scoring matrix profiles, secondary structure probabilities, monograms, bigram, position-specific estimated energy, half-sphere exposures, etc. Likewise, it explores well-known machine learning methods and proposes an optimized Light Gradient Boosting Machine Regressor (LightGBM) method, named TAFPred, to predict torsion angle fluctuations with the selected features. The proposed method achieves ten-fold cross-validated correlation coefficients of 0.746 and 0.737 and mean absolute errors of 0.114 and 0.123 for the angle fluctuation of φ and ψ, respectively, and attains an improvement of 10.08% in MAE, 24.83% in PCC in the phi angle, and 9.93% in MAE, 22.37% in PCC in psi angle compared to the state-of-the-art method proposed by Zhang et al.

The purpose of this study is to provide an accurate formula for calculating entropy for short DNA sequences and to demonstrate how to use it to examine leukemia patient surviving. We used IDIBAPS leukemia patient’s data base with 117 anonymized records. The generalized form of the Robust Entropy Estimator (EnRE) for short DNA sequences was proposed and key EnRE futures was showed. The Survival Analysis has been done using statistical package IBM SPSS. Entropy EnRE were calculated for leukemia patients for two samples: A. 2 groups divided by median EnRE and B. 2 groups of patients were formed according to their belonging to 1st and 4th quartiles of EnRE. The result of survival analysis are statistically significant: A. p < 0.05; B. p < 0.005. The death hazard for a patient with EnRE below median is 1.556 times that of a patient with EnRE over median and that the death hazard for a patient of 1st quartile (lowest EnRE) is 2.143 times that of a patient of 4th quartile (highest EnRE). The transition from median to quartile patients’ groups with more EnRE differentiation confirmed the unique significance of the entropy of DNA sequences for leukemia patients surviving.

In this paper, we introduce and study the notion of rough I₂-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I₂-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

For massive multiple-input multiple-output (MIMO) communications, the minimum mean square error (MMSE) scheme provides close to optimal recognition but involves inverting the high-dimensional matrix. A Gauss-Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing is introduced to address this problem. Firstly, the signal is initialized with the best of the three initialization regimes for faster algorithm convergence. Secondly, the signal is processed together with CJ. Finally, the pre-processed result is transferred to the GS detector. The simulation results indicate that the proposed iterative algorithm has a lower BER performance than the GS and improved iterative scheme based on GS in channels with different correlation levels.

Recently, deep learning models have been widely applied to modulation recognition, which have become a hot topic due to their excellent end-to-end learning capabilities. However, current methods are mostly based on uni-modal inputs, which suffer from incomplete information and local optimization. To complement the advantages of different modalities, we focus on the multi-modal fusion method. Therefore, we introduce an iterative dual-scale attentional fusion (iDAF) method to integrate multimodal data. Firstly, two feature maps with different receptive field sizes are constructed using local and global embedding layers. Secondly, the feature inputs are iterated into the Iterative Dual Scale Attention Module (iDCAM), where the two branches capture the details of high-level features and the global weights of each modal channel, respectively. The iDAF not only extracts the recognition characteristics of each specific domains, but also complements the strengths of different modalities to obtain a fruitful view. Our iDAF achieves a recognition accuracy of 93.5\% at 10dB and 0.6232 at full SNR. The comparative experiments and ablation studies effectively demonstrate the effectiveness and superiority of the iDAF.

In this paper, a new multi parameter iterative algorithm is proposed to address the PageRank problem based on the multi-splitting iteration method described by Gu et al . The proposed method in each iteration needs to solve two linear subsystems by splitting the coefficient matrix, therefore, we consider inner and outer iteration to find the approximate solutions of these linear subsystems. It can be shown that the iterative sequence generated by the multi parameter iterative algorithm finally converges to the PageRank vector when the parameters satisfy the certain conditions. Numerical experiments show that the proposed algorithm has better convergence and numerical stability than the existing algorithms.

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of linear programming problem. The optimal path refers to a path of minimum length according to the Euclidean metric. The apex method is based on the predictor-corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. Also, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

The most common source of transformer failure is in the insulation, and the most prevalent warning signal for insulation weakness is partial discharge (PD). Locating positons of these partial discharges would help repair the transformer to prevent failures. This work investigates algorithms that could be deployed to locate the position of a PD event using data from ultra-high frequency (UHF) sensors inside the transformer. These algorithms typically proceed in two steps: first determine the signal arrival time and then locate the position based on time differences. This paper reviews available methods for each task and then propose new algorithms: a convolutional iterative filter with thresholding (CIFT) to determine the signal arrival time and a reference table of travel times to resolve the source location. The effectiveness of these algorithms are tested with a set of laboratory-triggered PD events and two sets of simulated PD events inside transfers in production use. Tests show the new approach provides more accurate locations than the best-known data analysis algorithms, and the difference is particularly large, 3.7X, when the signal sources are far from sensors.

Abstract: Antimicrobial peptides (AMPs) are short peptides, usually made up of less than 100 amino acid residues. They are found in many living organisms and are an important factor in their innate immune systems. AMPs can be extracted from various living sources including bacteria, plants, animals and even humans. They are usually cationic peptides with an amphiphilic structure, which allows them to easily bind and interact with the cellular membranes of viruses, bacteria, fungi and other pathogens. They can act against both Gram-negative and Gram-positive pathogens and have various modes of action against them. Some attack the pathogens membrane, while others target their intracellular organelles as well as their nucleic acids, proteins and metabolic pathways. A crucial area of use of AMPs is in their ability to help with emerging antibiotic resistance: some AMPs are active against resistant strains and are susceptible to peptide engineering. This review considers AMPs from three key sources: plants, animals and humans, as well as their modes of action and some AMPs sequences.

Our work uses Iterative Boltzmann Inversion (IBI) to study the coarse-grained interaction between 20 amino acids and the representative carbon nanotube CNT55L3. IBI is a multi-scale simulation method that has attracted the attention of many researchers in recent years. It can effectively modify the coarse-grained model derived from the Potential of Mean Force (PMF). IBI is based on the distribution result obtained by All-Atom molecular dynamics simulation, that is, the target distribution function, the PMF potential energy is extracted, and then the initial potential energy extracted by the PMF is used to perform simulation iterations using IBI. Our research results have gone through more than 100 iterations, and finally, the distribution obtained by coarse-grained molecular simulation (CGMD) can effectively overlap with the results of all-atom molecular dynamics simulation (AAMD). In addition, our work lays the foundation for the study of force fields for the simulation of the coarse-graining of super-large proteins and other important nanoparticles.

This research not only dedicated a less restrictive method of iteration-varying function for a learning control law to design a controller but also synchronize two nonlinear systems with free time-delay. In addition, the mathematical theory of system synchronization has proved rigorously and the theory verified through an example to demonstrate the behavior of each parameter in the theory. The design of a controller using the iterative learning control law is significant for robotic tracking. The controller in this research generates a feed-forward control input using the error dynamics among the drive-response systems. The error dynamics satisfies the Lyapunov function and the combination of output errors, which respectively represented relative estimated differences of the drive-response systems. The iterative learning control rule serves the function of a filter adding previous control error after the end of each iteration. The numerical example of a synchronous system is given a Lorenz system for driving and another with the iterative learning control law for response under different initial condition. The results verify and demonstrate the proposed mathematical theory. The simulation exhibits consistency in the behavior of each parameter to match mathematical theory.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying frequencies (or probabilities) of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by natural number n (n = 1, 2, 3, 4,…). Correspondingly each epi-chain of order n ≥ 2 contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly discover that in long single-stranded and double-stranded DNA of any tested genome its DNA epi-chains of different orders n (values n are not too large) have practically identical frequencies (or probabilities) of each kind of nucleotides. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide frequencies on epi-chains of long DNA sequences are formulated for further their tests on a wider set of genomes. These results testify on existence of long-range coherence in long DNA and remind the Fröhlich's theory of long-range coherence in biological systems. The phenomenological data are discussed from different standpoints: the DNA double helices and helical antennas with circular polarizations of electromagnetic waves; relations with the Fröhlich's theory; numerical analysis of DNA epi-chains under binary representations of nucleotides. Results are useful for developing quantum and algebraic biology.

The Marchenko method is a data-driven way which makes it possible to calculate Green's functions from virtual points in the subsurface by the reflection data at the surface, only requiring a macro velocity model. This method requires collocated sources and receivers. However, in practice, subsampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green's functions. To solve this problem, this paper proposes to integrate sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply sparse inversion during the iterative process. Our work not only reduces the strict requirements on acquisition geometries, but also avoids the complexity and instability of direct inversion for Marchenko equations. This new method is applied to a two-dimensional numerical example with irregular sampled data. The result shows that it can effectively fill gaps of the obtained focusing functions and Green's functions in the Marchenko method.

There are some limitations in the null test measurement in the stitching interferometry. In order to meet the null test conditions, the moving distance between the sub-apertures often deviates from the theoretical preset distance, which leads to a position deviation of sub-apertures under measurements. To overcome this problem, an algorithm for data processing is proposed. We used iterative calculation of the deviations between the sub-apertures to adjust their positions, to ensure the local validity of the linear approximation algorithm and realize the exact stitching. A cylindrical lens as an object for experimental examination of the proposed method was taken. The obtained results demonstrate the validity, reliability and feasibility of our iterative stitching algorithm.

Water is essential to all life-forms including various ecological, geological, hydrological, and climatic processes/activities. With changing climate, associated El Nino/Southern Oscillation (ENSO) events appear to stimulate highly uncertain patterns of precipitation (P) and evapotranspiration (EV) processes across the globe. Changes in P and EV patterns are highly sensitive to temperature variation and thus also affecting natural streamflow processes. This paper presents a novel suite of stochastic modelling approaches for associating streamflow sequences with climatic trends. The present work is built upon a stochastic modelling framework HMM_GP that integrates a Hidden Markov Model with a Generalised Pareto distribution for simulating synthetic flow sequences. The GP distribution within HMM_GP model is aimed to improve the model's efficiency in effectively simulating extreme events. This paper further investigated the potentials of Generalised Extreme Value Distribution (EVD) coupled with an HMM model within a regression-based scheme for associating impacts of precipitation and evapotranspiration processes on streamflow. The statistical characteristic of the pioneering modelling schematic has been thoroughly assessed for their suitability to generate/predict synthetic river flows sequences for a set of future climatic projections. The new modelling schematic can be adapted for a range of applications in the area of hydrology, agriculture and climate change.

This article presents an analysis of monthly precipitation totals based on the Global Precipitation Climatology Centre database and monthly mean temperatures based on National Oceanic and Atmospheric Administration data for 377 catchments located around the world. Data sequences covering 110 years from 1901 to 2010 were analysed. The long-term sequences of precipitation and temperature were used to assess the variability of climate extremes, referred to here as polarisation. Measures of polarisation used in the natural sciences are discussed. A simple measure of polarisation was presented and applied to long-term sequences of monthly precipitation totals and monthly mean temperatures. Due to the nature of the proposed polarisation measure, other characteristics of precipitation and temperature sequences are also presented as a background for the discussion of the polarisation index. The study showed the existence of trends related to the polarisation of temperature and precipitation phenomena. As a result of the analysis, trends of polarisation factors in the area of precipitation and temperature were identified in 11 catchments out of the 377 analysed catchments. The trend analysis used Mann-Kendall tests at a level of significance of 5%. The Pettitt test was used to determine the point of trend change for precipitation and temperature data. The whole investigation is supported by rich graphical analyses, and the results are presented in tabular form.

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

In this article, an iterative method of two step is proposed for finding all roots simultaneously of polynomial equations. The order of convergence of the proposed algorithm is 2m, by using any iterative scheme of order m. Numerical tests are performed to confirm the theoretical results and to compare the proposed scheme with existing methods for finding all roots simultaneously.

The 3x+1 problem is a problem of continuous iteration for integers. According to the basic theorem of arithmetic and the way of iteration, we derive a general formula for continuous iteration for odd integers. Through this formula, we can construct a loop iteration equation and obtain the result of the equation: the equation has only one positive integer solution. In addition, this general formula can be converted into a linear indeterminate equation. The process of solving this equation shows that the relationship between the iteration result and the odd number being iterated is linear. Extending this result to all positive even numbers, we get the answer to the 3x + 1 question.

Impulsive noise is the main limiting factor for transmission over channels affected by electromagnetic interference. We study the estimation of (correlated) Gaussian signals in an impulsive noise scenarios. In this work, we analyze some of the existing as well as some novel estimation algorithms. Their performance is compared, for the first time, for different channel conditions, including the Markov-Middleton scenario, where the impulsive noise switches between different noise states. Following a modern approach in digital communications, the receiver design is based on a factor graph model and implements a message passing algorithm. The correlation among signal samples as well as among noise states brings about a loopy factor graph, where an iterative message passing scheme should be employed. As it is well known, approximate variational inference techniques are necessary in these cases. We propose and analyze different algorithms and provide a complete performance comparison among them, showing that both Expectation Propagation, Transparent Propagation, and the Parallel Iterative Schedule approaches reach a performance close to the optimal, at different channel conditions.

We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the reference fingerprint map (RFM). Spatial filtering and kernel smoothing of the kinematically collected raw data allow efficiently estimating the standard deviations during RFM generation. In the positioning stage, the weights control the contribution of each feature to the dissimilarity measure, which in turn quantifies the difference between the set of online measured features and the fingerprints stored in the RFM. Features with little variability contribute more to the estimated position than features with high variability. Iterations are necessary because the variability depends on the location, and the location is initially unknown when estimating the position. Using real WiFi signal strength data from extended test measurements with ground truth in an office building, we show that the standard deviations of these features vary considerably within the region of interest and are neither simple functions of the signal strength nor of the distances from the corresponding access points. This is the motivation to include the empirical standard deviations in the RFM. We then analyze the deviations of the estimated positions with and without the location-dependent weighting. In the present example the maximum radial positioning error from ground truth are reduced by 40% comparing to kNN without the weighted dissimilarity measure.

This paper presents a new adaptive and optimal algorithm for the trajectory tracking control of a quadrotor using iterative learning algorithm (ILA) and enumerative learning algorithm. Ordinarily the ILA, as an adaptive method, can perform well with PID control to improve the controller’s performance for a nonlinear system. Quadrotors are considered as non-linear and unstable systems which the use of an adaptive and optimal controller can increase its stability and decrease error level. In this method, a PID controller is proposed for the outer and inner control loops of a quadrotor and the ILA is used to adapt PID control gains. Subsequently, an enumerative learning algorithm is used to optimize the learning rates of the ILA. For this purpose, at first, the dynamic model of the quadrotor is acquired. After that, the structure of the inner and outer control loops is defined. In the end, the simulation results for the trajectory tracking control of a quadrotor are demonstrated. Through simulation, it is concluded that as time increases, the performance of the suggested control method in trajectory tracking control becomes better and better and error signals convergence to zero.

Prime period sequences can serve as the fundamental tool to construct arbitrary composite period sequences. This is a review study of prime period perfect Gaussian integer sequence (PGIS). When cyclic group {1,2,…,N−1} can be partitioned into k cosets, where N=kf+1 is an odd prime number, the construction of a degree-(k+1) PGIS can be derived from either matching the flat magnitude spectrum criterion or making the sequence with ideal periodic autocorrelation function (PACF). This is a systematic approach of prime period N=kf+1 PGIS construction, and is applied to construct PGISs with degrees 1, 2, 3 and 5. However, for degrees larger than 3, matching either the flat magnitude spectrum or achieving the ideal PACF encounters a great challenge of solving a system of nonlinear constraint equations. To deal with this problem, the correlation and convolution operations can be applied upon PGIS of lower degrees to generate new PGIS with degree-4 and other higher degrees, e.g., 6, 7, 10, 11, 12, 14, 20 and 21 in this paper. In this convolution based scheme, both degree and pattern of a PGIS vary and can be indeterminant, which is rather nonsystematic compared with the systematic approach. The combination of systematic and nonsystematic schemes contributes the great efficiency for constructing abundant PGISs with various degrees and patterns for the associated applications.

Optical motion capture is a mature contemporary technique for the acquisition of motion data, alas it is non-error-free. Due to technical limitations and occlusions of markers, gaps might occur in such recordings. The article reviews various neural network architectures applied for gap filling problem in motion capture sequences within FBM framework providing the representation for body kinematic structure. The results are compared with interpolation and matrix completion methods. We found out, that for longer sequences simple linear feedforward neural networks can outperform the other, sophisticated architectures. We were also able to identify, that acceleration and monotonicity of input sequence are the parameters that have a notable impact on the obtained results.

Multi-receiver encryption enables a sender to encrypt a message and transmit the ciphertext to a set of authorized users, while no one out this group of authorized users can decrypt the message. Multi-receiver encryption is of great importance in many sectors such as broadcast communication, cloud computing, wireless communications, networking applications, e-voting, lottery, and medical applications. This paper proposes an efficient multi-receiver public key encryption scheme based on Lucas sequences. The results of the computational analysis show that, projected scheme is better against renown attacks and prevailing anonymous multireceiver algorithms

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.

In this paper we evaluate the effects of hard and soft constraints on the Iterative Data Snooping (IDS), an iterative outlier elimination procedure. Here, the measurements of a levelling geodetic network were classified according to the local redundancy and maximum absolute correlation between the outlier test statistics, referred to as clusters. We highlight that the larger the relaxation of the constraints, the higher the sensitivity indicators MDB (Minimal Detectable Bias) and MIB (Minimal Identifiable Bias) for both the clustering of measurements and the clustering of constraints. There are circumstances that increase the family-wise error rate (FWE) of the test statistics, increase the performance of the IDS. Under a scenario of soft constraints, one should set out at least three soft constraints in order to identify an outlier in the constraints. In general, hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. In that process, one should opt to set out the redundant hard constraints. After identifying and removing possible outliers, the soft constraints should be employed to propagate their uncertainties to the model parameters during the process of least-squares estimation.

In this work, we present a new way to study the genetic code mathematical and chemical structure, based on the use of mathematical computations involving some few recently designed Fibonacci-like sequences, the “seeds” (“initial conditions”) of which are chosen according to the chemical and physical data of the three amino acids serine, arginine and leucine, playing a prominent role in a recent symmetry classification scheme of the genetic code. It appears that these mathematical sequences, of the same kind as the famous Fibonacci series, apart from their usual recurrence relations, are highly interwinned by many useful linear relationships. Using these sequences and also various sums or linear combinations of them, we derive several physical and chemical quantities of interest, as the number of total coding codons, 61, obeying various degeneracy patterns, the detailed number of hydrogen atoms, the detailed number of atoms (H/CNOS) and the integer molecular mass (or nucleon number), in the side chains of the 61 “amino acids”, also in various degeneracy patterns, in agreement with those described in the literature. Also, unexpectedly but interestingly, we find, as a by-product, an accurate description of the very chemical structure of the four ribonucleotides uridine monophosphate (UMP), cytidine monophosphate (CMP), adenosine monophosphate (AMP) and guanosine monophosphate (GMP), the building blocks of RNA whose groupings, in three units, constitutes the triplet codons. In summary, we find a full mathematical and chemical connection with the “ideal sextet’s classification scheme” mentioned above as well as with several others, notably, the Findley-Findley-McGlynn symmetrical classification. We organize the content of the text in such a way that, besides the presentation of several new research results, it has also an educational dimension. The paper could therefore be read and the computations easily worked out, also by non-experts with mathematical background.

The article presents an analysis of monthly precipitation totals based on the GPCC database, and monthly mean temperatures (NOAA data) for 377 catchments distributed across the globe. The analysis included 110-year data sequences from 1901 to 2010 calculated from grid data with a spatial resolution of 0.5°x 0.5° longitude and latitude. Long-term sequences of precipitation and temperature were used to assess the polarization of climatic phenomena. The noticeable impact of polarization in the area of extreme changes in temperature and precipitation is related to anthropogenic factors such as greenhouse gas emissions, deforestation and pollution, which affect ecosystem functioning, biodiversity, water resources and economies. The paper demonstrates the existence of trends related to the polarization of temperature and precipitation phenomena. The measures of polarization used in science are discussed. A simple measure of polarization was proposed and applied to both long-term sequences of monthly precipitation totals and monthly mean temperature. Due to the nature of the proposed polarization measure, other characteristics of the precipitation and temperature sequences are also presented as background for the discussion of the polarization index. The paper presents, for a selection of several hundred catchments from around the world, analyses of the assessment of precipitation and temperature trends using non-parametric tests. The trend analyses use Mann -Kendall tests at the 5% significance level. A Pettitt test was used to determine the trend change point for precipitation and temperature data. The whole is supported by rich graphical analyses and the results are presented tabularly.

Inherited mutations in BRCA1 and BRCA2 genes increase risks for breast, ovarian, and other cancers. Both genes encode proteins for accurately repairing chromosome breaks. If mutations inactivate this function, broken chromosomes may not be restored correctly, allowing breaks to persist or rearrange chromosomes. These abnormalities are potentially catastrophic events that can originate from viral infections. I used bioinformatic analyses of publicly available breast cancer patient data to show that the distribution of chromosome breaks in hereditary breast cancers differs markedly from sporadic breast cancers. Then I tested hereditary breast cancer sequence data around chromosome breaks for DNA similarity to all known viruses. Human DNA flanking breakpoints usually had decisive matches to Epstein-Barr virus (EBV / HHV4) tumor variants HKHD40 and HKNPC60. Many breakpoints were near EBV genome anchor sites, human EBV tumor-like sequences, EBV-associated epigenetic marks, and some fragile sites. On chromosomes 2 and 12, sequences near EBV genome anchor sites accounted for 90% and 88% of breakpoints (p<0.0001), respectively. On chromosome 4, 51/52 inter-chromosomal breakpoints were close to EBV-like sequences in 19 hereditary breast cancers. In contrast, 19 sporadic breast cancers only had 12 interchromosomal breakpoint regions on chromosome 4 near EBV-like sequences. On various other chromosomes, five EBV genome anchor sites were near hereditary breast cancer breakpoints at precisely defined, disparate gene or LINE locations. Independent evidence further implicating EBV in hereditary breast cancer breakpoints is that 25 breast cancer break positions are within 1.25% of breakpoints in model EBV cancers. In addition to BRCA1 or BRCA2 mutations, all the hereditary breast cancers had mutated genes essential for immune responses. This compromise facilitates reactivation of herpes viruses which produce nucleases capable of breaking chromosomes. EBV also causes other deleterious effects: anchored EBV episomes can interfere with normal replication and obstruct DNA break repairs; even very early infection causes massive transcription changes. The results, therefore, imply proactive treatment and prevention of herpes viral infections may prevent some chromosome breaks and benefit BRCA mutation carriers.

Inherited mutations in BRCA1 and BRCA2 genes increase risks for breast, ovarian, and other cancers. Both genes encode proteins for accurately repairing chromosome breaks. If mutations inactivate this function, chromosome fragments may not be restored correctly. Resulting chromosome rearrangements can become critical breast cancer drivers. Because I had data from thousands of cancer structural alterations that matched viral infections, I wondered whether infections contribute to chromosome breaks and rearrangements in hereditary breast cancers. There are currently no interventions to prevent chromosome breaks because they are thought to be unavoidable. However, if chromosome breaks come from infections, they can be treated or prevented. I used bioinformatic analyses to test publicly available breast cancer sequence data around chromosome breaks for DNA similarity to all known viruses. Human DNA flanking breakpoints usually had the strongest matches to Epstein-Barr virus (EBV) tumor variants HKHD40 and HKNPC60. Many breakpoints were near sites that anchor EBV genomes, human EBV tumor-like sequences, EBV-associated epigenetic marks, and fragile sites. On chromosome 2, sequences near EBV genome anchor sites accounted for 90% of breakpoints (p<0.0001). On chromosome 4, 51/52 inter-chromosomal breakpoints were close to EBV-like sequences. Five EBV genome anchor sites were near breast cancer breakpoints at precisely defined, disparate gene or LINE locations. Breakpoint flanking regions resembled known EBV-cancers. Twenty-five breakpoints in breast cancers were within 1.25% of EBV cancer breakpoints. In addition to BRCA1 or BRCA2 mutations, all the breast cancers had mutated genes essential for immune responses. Because of this immune compromise, herpes viruses can activate and produce nucleases that break chromosomes. Alternatively, anchored viral episomes can obstruct break repairs, whatever the cause. The results, therefore, imply proactive treatment and prevention of herpes viral infections may prevent some chromosome breaks and benefit BRCA mutation carriers.

In this article/review, the selective interactions of several berberine and palmatine derivatives with various DNA G-quadruplex structures are reported. These derivatives were constructed starting from two natural compounds, berberine and palamatine, through specific synthetic passages following two different schemes for each of them and using several substituents. The details of these synthesis are also described. Indeed, the study of the interactions of these derivative compounds with various G-quadruplex forming sequences was carried out by means of various structural and biochemical techniques. The results show that the presence of suitable side chains are very useful to improve the interaction of the ligands with G-quadruplex structures. Thus, since G-quadruplex formation is promoted by these compounds, which have never been reported before, these may be tested as potential anticancer drugs.

Genus Clematis is one of the largest within Ranunculaceae. Here we report the chloroplast genome of two Clematis species, C. brachyura and C. trichotoma endemic to Korea. The chloroplast genome lengths of C. brachyura and C. trichotoma are 159,532 bp and 159,170 bp, respectively. Gene contents in the complete chloroplast genomes of these two Clematis species are identical to that of most Ranunculaceae and other angiosperms. However, our data results demonstrated that genus Clematis has inversion and rearrangement events concerning gene rps4 gene, rps16 to trnH region, and trnL to ndhC region, and IR regions expansion. Comparison of IR regions among Ranunculaceae species revealed that Clematis species contained six protein coding genes (infA, rps8, rpl14, rpl16, rps3, and rpl22) usually found in the long single copy (LSC) region of other species. Phylogenetic analysis demonstrated that genus Clematis is closely related to genus Ranunculus. Differences in repeat structure, substitution rates, and IR expansion in genera Clematis and Ranunculus, explained their relationship. Clematis species showed slightly higher tandem repeats content than Ranunculus species. The six protein-coding genes showed lower synonymous substitution rates in the IR of Clematis species than in the LSC of Ranunculus species. Overall, the chloroplast genomes and results presented here provide important information on the evolution of Ranunculaceae.

We consider a coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared Patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. In this paper, an iterative list PRM projection algorithm is proposed to supplant the signal detector associated with the inner PRM sequences. In particular, we first propose an enhanced paths-saving algorithm called list PRM projection detection for the single-user scenario that keeps multiple candidates for the first few layers to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for the multi-user scenario. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verified that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ the iterative list detection to two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

Recently, a layer-stacked ESN model named deep echo state Network (DeepESN) has been established. As an interactional model of recurrent neural network and deep neural network, investigations of DeepESN are of significant importance in both areas. Optimizing the structure of neural networks remains a common task in artificial neural networks, and the question of how many neurons should be used in each layer of DeepESN must be stressed. In this paper, our aim is to solve the problem of choosing the optimized size of DeepESN. Inspired by the sensitive iterative pruning algorithm, a neuronal similarity-based iterative pruning merging algorithm (NS-IPMA) is proposed to iteratively prune or merge the most similar neurons in DeepESN. Two chaotic time series prediction tasks are applied to demonstrate the effectiveness of NS-IPMA. The results show that the DeepESN pruned by NS-IPMA outperforms unpruned DeepESN with the same network size, and NS-IPMA is a feasible and superior approach to improving the generalization performance of DeepESN.

The node position information is critical in the wireless sensor network (WSN). However, the existing positioning algorithms commonly have low positioning accuracy because of noise interferences in communication. To solve this problem, this paper presents an iterative positioning model based on distance correction to improve the positioning accuracy of the target node in WSN. First, the log-distance distribution model of received signal strength indication (RSSI) ranging is built and the noise impact factor is derived based on the model. Second, the initial position coordinates of the target node are obtained based on the triangle centroid localization algorithm, thereby calculating the distance deviation coefficient under the influence of noise. Then, the ratio of the distance measured by the log-normal distribution model to the median distance deviation coefficient is taken as the new distance between the anchor node and the target node. Based on the new distance, the triangular centroid positioning algorithm is used again to calculate the target node coordinates. Finally, the iterative positioning model is constructed, and the distance deviation coefficient is updated repeatedly to update the positioning result until the set number of iterations is reached. Experiment results show that the proposed iterative positioning model can improve positioning accuracy effectively.

Empirical Colebrook equation from 1939 is still accepted as an informal standard to calculate friction factor during the turbulent flow (4000 < Re < 10⁸) through pipes from smooth with almost negligible relative roughness (ε/D→0) to the very rough (up to ε/D = 0.05) inner surface. The Colebrook equation contains flow friction factor λ in implicit logarithmic form where it is, aside of itself; λ, a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D; λ = f (λ, Re, ε/D). To evaluate the error introduced by many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate value of the friction factor λ from the Colebrook equation as accurate as possible. The most accurate way to achieve that is using some kind of iterative methods. Usually classical approach also known as simple fixed point method requires up to 8 iterations to achieve the high level of accuracy, but does not require derivatives of the Colebrook function as here presented accelerated Householder’s approach (3^rd order, 2^nd order: Halley’s and Schröder’s method and 1^st order: Newton-Raphson) which needs only 3 to 7 iteration and three-point iterative methods which needs only 1 to 4 iteration to achieve the same high level of accuracy. Strategies how to find derivatives of the Colebrook function in symbolic form, how to avoid use of the derivatives (Secant method) and how to choose optimal starting point for the iterative procedure are shown. Householder’s approach to the Colebrook’s equations expressed through the Lambert W-function is also analyzed. One approximation to the Colebrook equation based on the analysis from the paper with the error of no more than 0.0617% is shown.

In the context of all-digital radar systems, phase-modulated continuous wave (PMCW) based on pseudorandom binary sequences (PRBSs) appears a prominent candidate modulation scheme for applications such as autonomous driving. Among the reasons for that are its simplified transmitter architecture and lower linearity requirements, e.g., compared to orthogonal-frequency division multiplexing radars, as well as its high velocity unambiguity and multiple-input multiple-output operation capability that are characteristic of digital radars. For appropriate operation of a PMCW radar, choosing a PRBS whose periodic autocorrelation function (PACF) has low sidelobes and high robustness to Doppler shifts is paramount. In this sense, this article performs an analysis of Doppler shift tolerance of the PACFs of typically adopted PRBSs in PMCW radar systems supported by simulation and measurement results. To accurately measure the Doppler-shift-induced degradation of PACFs, peak power loss ratio (PPLR), peak sidelobe level ratio (PSLR), and integrated-sidelobe level ratio (ISLR) were used as metrics. Furthermore, to account for effects on targets whose ranges are not multiples of the range resolution, oversampled PACFs are analyzed.

The aim of this survey is to review some recent developements in devising efficient preconditioners for sequences of linear systems A x = b. Such a problem arise in many scientific applications, such as discretization of transient PDEs, solution of eigenvalue problems, (Inexact) Newton method applied to nonlinear systems, rational Krylov methods for computing a function of a matrix. Full purpose preconditioners such as the Incomplete Cholesky (IC) factorization or approximate inverses are aimed at clustering eigenvalues of the preconditioned matrices around one. In this paper we will analyze a number of techniques of updating a given IC preconditioner (which we denote as P0 in the sequel) by a low-rank matrix with the aim of further improving this clustering. The most popular low-rank strategies are aimed at removing the smallest eigenvalues (deflation) or at shifting them towards the middle of the spectrum. The low-rank correction is based on a (small) number of linearly independent vectors whose choice is crucial for the effectiveness of the approach. In many cases these vectors are approximations of eigenvectors corresponding to the smallest eigenvalues of the preconditioned matrix P0 A. We will also review some techniques to efficiently approximate these vectors when incorporated within a sequence of linear systems all possibly having constant (or slightly changing) coefficient matrices. Numerical results concerning sequences arising from discretization of linear/nonlinear PDEs and iterative solution of eigenvalue problems show that the performance of a given iterative solver can be very much enhanced by the use of low-rank updates.

Aim: Streptococcus pneumoniae and influenza H1N1 virus are common organisms associated with human infections. These infections could play a significant role in immune regulation. The study was performed to analyse the genome sequences of these organisms with human genome and study its functional significance. Methods: The study was performed to analyse the overlapping of genome sequences in Streptococcus pneumoniae and Influenza (H1N1) virus against human genome sequences by BLASTn sequence analysis. The alignments are studied against the corresponding genes for their functional significance with DAVID and NDEx software.Results: Several hits or overlapping nucleotide segments were identified. Between streptococcus and homo sapiens 287 overlaps were identified, and among influenza and homo sapiens 124 hits were identified. A wide range of functional significance of these genes were identified, and the results are presented in this study. The results show insights into functional pathways and biological activities associated with the respective vaccinations or infections by these microorganisms. Conclusion: The common organisms like Streptococcus pneumoniae and Influenza H1N1 virus actively interact with the immune system and result in a wide range of immune regulations.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

The steel damper column is an energy-dissipating member that is suitable for reinforced concrete (RC) buildings, and those used for multistory housing in particular. However, the effectiveness of steel damper columns may be affected by the behavior of surrounding members, and this effect can be severe in the case of seismic sequences. This article investigates the nonlinear response of building models having an RC moment-resisting frame (MRF) with and without steel damper columns under seismic sequences. The applicability of the concept of the momentary energy input to the prediction of the peak response of RC MRFs with damper columns under seismic sequences is also investigated. The main findings of the study are summarized as follows. (1) The peak response of RC MRFs with damper columns subjected to sequential accelerations is similar to the peak response obtained considering only the mainshock, whereas the cumulative strain energy of RC MRFs accumulates more for sequential accelerations. (2) The steel damper column is effective in reducing the peak and cumulative responses of RC MRFs in the case of sequential seismic input. (3) The relation of the hysteretic dissipated energy during a half cycle of the structural response and the peak displacement of the first modal response can be properly evaluated using the simple model proposed in this study.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.

We hypothesize that the first ancestral "ante-cell" molecular structures, i.e., first RNAs and peptides which gradually transformed into real cells once the Earth had cooled sufficiently for organic molecules to appear there, have leaved traces in RNAs and genes of present cells. We propose a circular RNA which could have been one of these ancestral structures whose vestigial pentameric subsequences would mark the evolution from this key moment when the ante-cells have begun to join the living organisms. In particular, we propose that in present RNAs (ribosomal or messenger) playing an important role in the metabolism of current cells, we look for traces of the proposed primitive structure in the form of pentamers (or longer fragments) belonging to their nucleotide sequence. The result obtained can be summarized in the existence of a gradient of occurrence of such pentamers, with a high frequency for the most vital functions (protein synthesis, nucleic synthesis, cell respiration, etc.). This gradient is also visible between organisms, from the oldest (Archaea) to the most recent (Eukaryotes) in evolution of species.

We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless finite-state encoder that compresses the reconstruction codeword with no additional distortion. We first derive two different lower bounds to the compression ratio that depend on the number of states of the lossless encoder. Both bounds are asymptotically achievable by conceptually simple coding schemes. We then show that when the number of states of the lossless encoder is large enough in terms of the reconstruction block-length, the performance can be improved, sometimes significantly so. In particular, the improved performance is achievable using a random-coding ensemble that is universal, not only in terms of the source sequence, but also in terms of the distortion measure.

In Southeast Asia, the incidence of Leukemia, a malignant blood cancer originating from hema-topoietic progenitor cells, is on the rise, marked by a concerning 54% mortality rate. This study focuses on enhancing early-stage prediction to improve patient recovery prospects significantly. Leveraging Machine Learning and Data Science, we employ protein sequential data from frequently mutated genes such as BCL2, HSP90, PARP, and RB to predict Chronic Myeloid Leukemia (CML). Our approach relies on robust feature extraction techniques, namely Di-peptide Composition (DPC), Amino Acid Composition (AAC), and Pseudo amino acid composition (Pse-AAC), with prior attention to addressing outliers and validating feature selection through the Pearson Corre-lation Coefficient. Data augmentation ensures a well-rounded dataset for analysis. Employing a range of Machine Learning models, including Support Vector Machine (SVM), XGBoost, Random Forest (RF), K Nearest Neighbor (KNN), Decision Tree (DT), and Logistic Regression (LR), we achieve accuracy rates spanning from 66% to 94%. These classifiers undergo comprehensive as-sessment using performance metrics such as accuracy, sensitivity, specificity, F1-score, and the confusion matrix. Our proposed solution, encompassing a user-friendly web application dashboard, presents an invaluable tool for early CML diagnosis with profound implications for practitioners, offering a deploy-able asset within healthcare institutions and hospitals.

In the process of transcription initiation by RNA polymerase, promoter DNA sequences affect multiple reaction pathways determining the productivity of transcription. However, the question of how the molecular mechanism of transcription initiation depends on sequence properties of promoter DNA remains poorly understood. Here, combining the statistical mechanical approach with high-throughput sequencing results, we characterize abortive transcription and pausing during transcription initiation by Escherichia coli RNA polymerase at a genome-wide level. Our results suggest that initially transcribed sequences enriched with thymine bases represent the signal inducing abortive transcription. On the other hand, certain repetitive sequence elements broadly embedded in promoter regions constitute the signal inducing pausing. Both signals decrease the productivity of transcription initiation. Based on solution NMR and in vitro transcription measurements, we also suggest that repetitive sequence elements of promoter DNA modulate the rigidity of its double-stranded form, which profoundly influences the reaction coordinates of the productive initiation via pausing.

This study assessed the performance of low-dose CT lung scans across various acquisition parameters and examined the impact of iterative reconstruction (IR) algorithms on image quality for lung cancer screening. The performance of multi-slice CT scanners was assessed by using a Catphan 600 phantom, specifically within the CTP404 test module that contains materials like Teflon, Delrin, Acrylic, Polystyrene, LDPE, PMP, Air, and water. Three protocols were selected and categorized into standard, low dose, and ultra-low dose. The standard protocol featured a tube voltage of 100 kVp for single-detector CT, a pitch of 0.75, detector collimation of 0.60 mm, and a gantry rotation time of 0.33 seconds, with 5 mm slice thickness. Images were reconstructed using standard kernels like B80f and 170f, combined with either FBP or various IR algorithms. Findings indicated that the noise power spectrum (NPS) peak value (HU2mm2) increased with higher IR levels, with FBP showing the highest peak. Additionally, NPS spatial frequency diminished as IR levels rose. Optimizing contrast and spatial resolution for both background and regions of interest involved adjusting the target transfer function (TTF) and contrast-to-noise ratio (CNR), crucial for protocol optimization. Proper adjustment of IR levels is vital, as higher levels can alter image texture and affect NPS spatial frequency. The results of this study showed that the use of IR algorithms in low-dose CT lung scans significantly improved image quality, particularly in terms of noise reduction and spatial resolution. However, the choice of acquisition parameters also played a crucial

This paper presents the design of a new neuro-generator of pseudorandom number type PRNG Pseudorandom Number Generator, which produces complex sequences with an adequate bit distri-bution. The circuit is connected to a neuronal module with six impulse neurons with different be-haviors: spike frequency adaptation, phasic spiking, mixed mode, phasic bursting, tonic bursting and tonic spiking. This module aims to generate a non-periodic signal that becomes the clock sig-nal for one of the LFSRs Linear Feedback Shift Register that the neuro-generator has. To verify its correct operation, the neuro-generator was subjected to a series of tests where the frequencies of the impulse neurons were modified. This modification allows generating a greater number of pulses at the output of the neuronal module, to obtain sequences with different characteristics that pass different NIST statistical tests National Institute of Standards and Technology of U.S. The results show that the new neuro-generator maintains pseudo-randomness in the sequences obtained with different frequencies and it can be implemented on reconfigurable FPGA Field Programmable Gate Array Virtex 7 xc7vx85t-2ffg1761 device. Therefore, it can be used for applications such as biologi-cal systems.

The aim of this paper is to deep into the dynamic study of the well known Chebyshev-Halley family of iterative methods for solving nonlinear equations. Our objetives are twofold: one the one hand, we are interested in characterize the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in study the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have a bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where this two situations happen simultaneously. That is, the rational map obtained by applying a method in the Chebyshev-Halley family to a polynomial has both super-attracting extraneous fixed point and super-attracting cycles different to the roots of the polynomial.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ; λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

The exceptional increase in molecular DNA sequence data in open repositories is mirrored by an ever-growing interest among evolutionary biologists to harvest and use those data for phylogenetic inference. Many quality issues, however, are known and the sheer amount and complexity of data available can pose considerable barriers to their usefulness. A key issue in this domain is the high frequency of sequence mislabelling encountered when searching for suitable sequences for phylogenetic analysis. These issues include the incorrect identification of sequenced species, non-standardised and ambiguous sequence annotation, and the inadvertent addition of paralogous sequences by users, among others. Taken together, these issues likely add considerable noise, error or bias to phylogenetic inference, a risk that is likely to increase with the size of phylogenies or the molecular datasets used to generate them. Here we present a software package, phylotaR, that bypasses the above issues by using instead an alignment search tool to identify orthologous sequences. Our package builds on the framework of its predecessor, PhyLoTa, by providing a modular pipeline for identifying overlapping sequence clusters using up-to-date GenBank data and providing new features, improvements and tools. We demonstrate our pipeline’s effectiveness by presenting trees generated from phylotaR clusters for two large taxonomic clades: palms and primates. Given the versatility of this package, we hope that it will become a standard tool for any research aiming to use GenBank data for phylogenetic analysis.

In our article in Genome Biology Ecology six years ago, one complete plastid genome of Belian was assembled for comparative analyses of the plastomes in Lauraceae. However, Ariati et al. (2023) concluded that our sequenced Belian individual could be located in the clade of Myristicaceae instead of that of Lauraceae. Here, we performed re-analyses of additional two Belian plastomes, along with 42 plastomes from plants spanning ten families of the Magnoliids. The plastomes of the three Belian individuals range from 157,535 to 157,577 bp in length. Comparative genomic analysis revealed 170 mutation sites in their plastomes, which include 111 substitutions, 53 indels, and six microinversions. Phylogeny was reconstructed using maximum likelihood and Bayesian approaches for 44 magnoliids species indicated that our three Belian individuals are nested among the species in the family Lauraceae rather than Myristicaceae.

Advances in DNA sequencing technology are facilitating genomic analyses of unprecedented scope and scale, widening the gap between our abilities to generate and fully exploit biological sequence data. Comparable analytical challenges are encountered in other data-intensive fields involving sequential data, such as signal processing, in which dimensionality reduction (i.e., compression) methods are routinely used to lessen the computational burden of analyses. In this work we explore the application of dimensionality reduction methods to numerically represent high-throughput sequence data for three important biological applications of virus sequence data: reference-based mapping, short sequence classification and de novo assembly. Despite using highly compressed sequence transformations to accelerate the processes, our sequence processing approach yielded comparable accuracy to existing approaches, and are ideally suited for sequences originating from highly diverse virus populations. We demonstrate the application of our methodology to both synthetic and real viral pathogen sequence data. Our results show that the use of highly compressed sequence approximations can provide accurate results and that useful analytical performance can be retained and even enhanced through appropriate dimensionality reduction of sequence data.

We aimed to apply DNA barcoding tool for the molecular identification of horn snails T. telescopium using mitochondrial cytochrome oxidase I gene (mt-COI) and to investigate their evolutionary relationship along with location-specific bio-geographical variations. The molecular data sets of this study indicate that strong probability of T. telescopium species taxonomic confirmation using mt-COI sequences. Results of the phylogenetic analysis suggest that Telescopium sp. was monophyletic with disseminated nodes and the evolution of group II originated from group I. The substantial genetic distance among the mt-COI sequences (0.005 to 0.184) were noticed. Large divergence between the south-west coast of India and Australia region population indicates limited gene flow between the two continents. Our study suggests that the genera Telescopium is globally ubiquitous but genetically showing inter-region differentiation. We conclude that mt-COI gene can be used to identify gastropod T. telescopium species.

In this paper, we generalize the concept of I-statistical convergence, which is a recently introduced summability method, with an infinite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our definitions. The name of our new method will be A^{I}-lacunary statistical convergence with respect to a sequence of modulus functions. We also define strongly A^{I}-lacunary convergence and we give some inclusion relations between these methods.

Ajuga arabica is an essential medicinal plant found naturally in Saudi Arabia, recognized for its therapeutic characteristics. Nevertheless, research on the genetic diversity and population arrangement of this species in Saudi Arabia is deficient. In this study, we conducted a comparative examination of DNA and gene sequences to evaluate the genetic diversity and population configuration of Ajuga arabica in Saudi Arabia. Our findings demonstrate that there are high levels of genetic diversity within populations, but low levels of genetic differentiation among populations. Moreover, we discovered proof of gene flow among populations, suggesting that there are no significant genetic barriers to gene flow. Our results offer valuable insights into the genetic diversity and population structure of Ajuga arabica in Saudi Arabia, which can support conservation efforts and promote the sustainable use of this valuable medicinal plant.

In the Versatile Video Coding (VVC) standard, affine motion models have been applied to enhance the resolution of complex motion patterns. However, due to the high computational complexity involved in affine motion estimation, real-time video processing applications face significant challenges. This paper focuses on optimizing affine motion estimation algorithms in the VVC environment and proposes a fast gradient iterative algorithm based on edge detection for efficient computation. Firstly, we establish judging conditions during the construction of affine motion candidate lists to streamline the redundant judging process. Secondly, we employ the Canny edge detection method for gradient assessment in the affine motion estimation process, thereby enhancing the iteration speed of affine motion vectors. Experimental results demonstrate that our affine motion estimation algorithm reduces encoding time by approximately 15%-35% while maintaining video bitrate and quality.

As time progresses and technology improves, biological data sets are continuously increasing in size. New methods and new implementations of existing methods are needed to keep pace with this increase. In this paper, we present a high performance computing(HPC)-capable implementation of Iterative Random Forest (iRF). This new implementation enables the explainable-AI eQTL analysis of SNP sets with over a million SNPs. Using this implementation we also present a new method, iRF Leave One Out Prediction (iRF-LOOP), for the creation of Predictive Expression Networks on the order of 40,000 genes or more. We compare the new implementation of iRF with the previous R version and analyze its time to completion on two of the world's fastest supercomputers Summit and Titan. We also show iRF-LOOP's ability to capture biologically significant results when creating Predictive Expression Networks. This new implementation of iRF will enable the analysis of biological data sets at scales that were previously not possible.

The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article.

In this paper, we first investigate secure communications for a two-hop interference relay system in the wireless Internet of Things (IoT), where K source-destination pairs communicate in the presence of an eavesdropper. Explicitly, we jointly design source, relay and destination matrices upon minimizing total mean-squared error (MSE) of all legitimate destinations while keeping the MSE at eavesdropper above a certain threshold. We illuminate that the joint design of the source, relay and destination matrices subject to both secrecy and transmit power constraints. More specifically, we proposed an efficient iterative distributed algorithm to simplify the process of the joint design for optimal source, relay and destination matrices. Furthermore, the convergence of the iterative distributed algorithm is described. Additionally, the performances of the proposed algorithm, including both its secrecy rate and MSE, are characterized with the aid of simulation results. We demonstrate that our proposed algorithm outperforms the traditional approach. As a benefit, secure communications can be guaranteed by using the proposed algorithm for the multiple input multiple output (MIMO) interference relay IoT network in the presence of an eavesdropper.

The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ; . It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

In this paper, we present a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations. After the convergence analysis, we study the stability of this class by using the tools of complex discrete dynamics. This allows us to select those elements of the class with lower dependence on initial estimations. We verify by means of numerical tests that the stable members on quadratic polynomials perform better than the unstable ones, when applied to other non-polynomial functions. We also compare the performance of the best elements of the family with known methods, such as the schemes by Newton or Chun, among others, showing robust and stable behaviour.

In celIs, microtubule location, length, and dynamics are regulated by a host of microtubule-associated proteins and enzymes that read where to bind and act based on the microtubule “tubulin code,” which is predominantly encoded in the tubulin carboxy-terminal tail (CTT). Katanin is a highly conserved AAA ATPase enzyme that binds to the tubulin CTTs to remove dimers and sever microtubules. We have previously demonstrated that short CTT peptides are able to inhibit katanin severing. Here, we examine effects of CTT sequences on this inhibition activity. Specifically, we examine CTT sequences found in nature, alpha1A (TUBA1A), detyrosinated alpha1A, Δ2 alpha1A, beta5 (TUBB/TUBB5), beta2a (TUBB2A), beta3 (TUBB3), and beta4b (TUBB4b). We find that these natural CTTs have distinct abilities to inhibit, most noticeably beta3 cannot inhibit katanin. Two non-native CTT tail constructs are also unable to inhibit – despite having 94% sequence identity with alpha1 or beta5 sequences. Surprisingly, we demonstrate that poly-E and poly-D peptides are capable of inhibiting katanin significantly. An analysis of the hydrophobicity of the CTT constructs indicates that more hydrophobic polypeptides are less inhibitory than more polar polypeptides. These experiments not only demonstrate inhibition, but also likely interaction and targeting of katanin to these various CTTs when they are part of a polymerized microtubule filament.

Phenotypic complementation of gene knock-outs is an essential step in establishing function. Here we describe a simple strategy for ‘gold standard’ complementation in which the mutant allele is replaced in situ with a wild type (WT) allele in a procedure that exploits CRISPR/Cas9. The method relies on the prior incorporation of a unique 24 nucleotide (nt) ‘bookmark’ sequence into the mutant allele to act as a guide RNA target during its Cas9-mediated replacement with the WT allele. The bookmark comprises a 23 nt Cas9 target sequence plus an additional nt to ensure the deletion is in-frame. Here, bookmarks are tailored to Streptococcus pyogenes CRISPR/Cas9, but could be designed for any CRISPR/Cas system. For proof of concept, 9 bookmarks were tested in Clostridium autoethanogenum. Complementation efficiencies reached 91%. As complemented strains are indistinguishable from their progenitors, concerns over contamination may be satisfied by incorporation of ‘watermark’ sequences into the complementing genes.

One of the most significant developments in the sports world over the last two decades has been the use of mathematical methods in conjunction with the massive amounts of data now available to analyze performances, identify trends and patterns, and forecast results. Football analytics has advanced significantly in recent years and continues to evolve as it becomes a more recognized and integral part of the game. Football analytics is also used to forecast game outcomes, allowing bettors to make educated guesses. This article describes mathematical concepts related to football analytics that enable a better betting strategies. We explain how the pitch is partitioned into different zones and we define possession sequences. Furthermore, we explain what an expected goals model is and which expected goals model we use in this research. Furthermore, we define two general characteristics of a player evaluation method, each corresponding to one of the equations of the Dawson model. Based on these characteristics, we describe the developments of several general approaches for evaluating players in the context of the Dawson model.

This research is a preliminary phase of a general effort to develop a generic-data transferring capability via human haptic thermal sensation (generic-data refers to a coded language like Morse or Braille). For the capability to be effective, it must include a large variety of short recognizable cues. Hence, we propose the concept of cues based on sequences of thermal pulses, i.e., combinations of warm and cool pulses with several levels of intensity. The objective of this study was to determine the feasibility of basing a generic-data-transfer capability on thermal cues composed of sequences of short pulses. The research included defining the basic characteristics of the stimuli parameters and developing practical methods for generating and measuring them. Several sequences were designed in light of the relevant data known to date, and tests were conducted. The thermal cues presented to the participants were sensed and recognized by touch. The results indicate high feasibility for a capability that is applicable in various scenarios. In addition, the low impact on human skin temperature due to short stimuli duration represents an inherent advantage for later implementation. This report presents promising findings and offers insights for further investigation.

Quantum leaps advances in the single-molecule investigative science have been made possible over the past decades through the implication of nanopores, as versatile components on dedicated biosensors. Here, we employed the nanopore-tweezing technique to capture amino acid-functionalized, peptide-nucleic acids (PNA) with -hemolysin-based nanopores, and correlate the ensuing stochastic fluctuations of the ionic current through the nanopore with the composition and order of bases in the PNAs primary structure. We demonstrate that while the system enables detection of distinct bases on homopolymeric PNA or triplet bases on heteropolymeric strands, it also reveals rich insights into the conformational dynamics of the entrapped PNA within the nanopore, relevant for perfecting the recognition capability single-molecule sequencing.

An experimental ultra wideband ground penetrating radar based on Golay complementary sequences is proposed to locate underground pipes. Golay complementary sequences with the code length of 1024 and frequency of 1 GHz are used as the probe signals. Two-dimensional image of the buried pipes is achieved by correlation method and back projection algorithm. The experimental results show that both the plastic pipe and metallic pipe can be located with a range resolution of 10 cm. Furthermore, as the Golay complementary sequences are a pair of complementary sequences, the sum of their correlation function yields twice the value of the peak at the target position and zero elsewhere. Thus, compared with the stepped frequency signal radar or chaotic signal radar, the Golay-based radar can significantly improve the signal noise ratio and has capability of deep detection.

The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The PQ penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper we investigate all possible finite games that can be played between the two players Q and Picard of the original PQ game. For this purpose we establish a rigorous connection between finite automata and the PQ game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the PQ game. What this means is that from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

The genus Fritillaria belongs to the widely distributed family Liliaceae. The bulbs of Fritillaria ussuriensis and Fritillaria cirrhosa are valuable herbaceous medicinal ingredients. However, they are still used indiscriminately in herbal medicine. Identification and molecular phylogenic analysis of Fritillaria species is therefore required. Here, we report the complete chloroplast (cp) genome sequences of F. ussuriensis and F. cirrhosa. The two Fritillaria cp genomes were 151,524 and 151,083 bp in length, respectively, including a pair of inverted repeat regions (52,678 and 52,156 bp) separated by a large single copy region (81,732 and 81,390 bp) and small single copy region (17,114 and 17,537 bp). A total of 111 genes in F. ussuriensis and 112 in F. cirrhosa comprised 77 protein-coding genes in F. ussuriensis and 78 in F. cirrhosa, 30 tRNA genes, and four rRNA genes. The gene order, content, and orientation of the two Fritillaria cp genomes exhibited the general structure of flowering plants, and were similar to those of other Fritillaria species. Comparison of the six Fritillaria species’ cp genomes indicated seven highly divergent regions in intergenic spacers and in the matK, rpoC1, rpoC2, ycf1, ycf2, ndhD, and ndhF coding regions. We established the position of the six species through phylogenic analysis. The complete chloroplast genome sequences of two Fritillaria species will be useful genomics resources for identification of Fritillaria species and for studying the phylogenetic relationship among Fritillaria species within the Liliaceae family.

It is unavoidable that the characteristics of the robot system alter inexactly or cannot be correctly determined during movement and are impacted by external disturbances. There are many adaptive control methods, such as sliding control or neural control, to improve the quality of trajectory tracking for robot motion systems. Still, those methods require a large amount of computation related to solving the problem of constrained nonlinear optimization problem. The article presents some techniques for determining an intelligent controller's online learning function parameters, including two circuits: the inner circuit is a state feedback linearized controller, and the outer course is an Interactive learning controller and does not use the robot's mathematical mode with function parameters online optimal learning and intelligent online learning closely following the joint model to stabilize the robot system. Finally, the 2-DOF planar robot simulation is performed on Matlab software R2022b. The findings indicate that outstanding tracking performance is achievable.

Given the pathological role of hyperphosphorylated Tau aggregation in Alzheimer’s disease (AD) our laboratory previously developed the novel Tau aggregation inhibitor peptide, RI-AG03. As Tau aggregates accumulate intracellularly, it is essential that Tau-targeting peptides efficiently traverse the cell membrane. In addition, these peptides need to avoid sequestration into cell organelles, particularly those involved in degradation, to ensure interaction with Tau in the cytoplasm. Here, we examine the cellular uptake and intracellular trafficking of RI-AG03 when the peptide is unconjugated or linked to nanoliposome carrier particles. The impact of adding the cell penetrating peptide (CPP) sequences, polyarginine (polyR) and transactivator of transcription (TAT), to RI-AG03 was also characterised. Our data show that the conjugation of CPP-containing RI-AG03 to liposomes dramatically increases cellular liposomes uptake. The majority of this uptake occurs via direct cell penetration. However, we find that macropinocytosis is also an important mechanism for unconjugated and RI-AG03-polyR-conjugated, but not RI-AG03-TAT-conjugated, liposome uptake. In agreement with this macropinocytosis-mediated internalisation, liposome lipids localise to lysosomes and macropinosomes following cellular uptake. However, while unconjugated RI-AG03 peptides also localise to lysosomes, liposome conjugation prevents this localisation, with the peptide detaching from the liposomes at the cell surface and evading organelle entrapment. Overall, this study demonstrates that CPP sequences and nanoliposomes carriers enhance the intracellular delivery of RI-AG03, furthering the possibility of the peptide’s use in targeting Tau pathology in AD.

Examining the similarity of event environments or surroundings, more precisely settings, provides additional insight in analyzing event sequences as it provides information about the context and potential common factors that may have influenced them. This article proposes a new similarity measure for event setting sequences, which involve the space and time in which events occur. While similarity measures for spatiotemporal event sequences have been studied, the settings and setting sequences have not yet been studied. While modeling event setting sequences we consider spatial and temporal scales to define the bounds of the setting and incorporates dynamic variables alongside static variables. Using a matrix-based representation and an extended Jaccard index we developed new similarity measures that allow for the use of all variable data types. We successfully used these similarity measures coupled with other multivariate statistical analysis approaches in a case study involving setting sequences and pollution event sequences associated with the same monitoring stations, which validate the hypothesis that more similar spatial-temporal settings or setting sequences may generate more similar events or event sequences. In conclusion, these similarity measures have many potential real-world applications, and offer researchers a powerful tool for understanding different factors and their dynamics corresponding to occurrences of spatiotemporal event sequences.