Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

Robust digital image watermarking against shearing based on Haar orthogonal function system

In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks.

ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

Generalized Product of Iteration Function System

The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS） are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.

Simulation for chaos game representation of genomes by recurrent iterated function systems

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.

ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE

Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some ＂non-standard＂ multifractal structure, which contrasts the well-knoWn multifractal formalism for the invariant measure of system {S1,.., SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and MSrters-Shieh [12].

Iterated Function System-Based Crossover Operation for Real-Coded Genetic Algorithm

An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions.

Interaction between systemic iron parameters and left ventricular structure and function in the preserved ejection fraction population:a two-sample bidirectional Mendelian randomization study

BACKGROUND Left ventricular(LV)remodeling and diastolic function in people with heart failure(HF)are correlated with iron status;however,the causality is uncertain.This Mendelian randomization(MR)study investigated the bidirectional causal relationship between systemic iron parameters and LV structure and function in a preserved ejection fraction population.METHODS Transferrin saturation(TSAT),total iron binding capacity(TIBC),and serum iron and ferritin levels were extracted as instrumental variables for iron parameters from meta-analyses of public genome-wide association studies.Individuals without myocardial infarction history,HF,or LV ejection fraction(LVEF)<50%(n=16,923)in the UK Biobank Cardiovascular Magnetic Resonance Imaging Study constituted the outcome dataset.The dataset included LV end-diastolic volume,LV endsystolic volume,LV mass(LVM),and LVM-to-end-diastolic volume ratio(LVMVR).We used a two-sample bidirectional MR study with inverse variance weighting(IVW)as the primary analysis method and estimation methods using different algorithms to improve the robustness of the results.RESULTS In the IVW analysis,one standard deviation(SD)increased in TSAT significantly correlated with decreased LVMVR(β=-0.1365;95%confidence interval[CI]:-0.2092 to-0.0638;P=0.0002)after Bonferroni adjustment.Conversely,no significant relationships were observed between other iron and LV parameters.After Bonferroni correction,reverse MR analysis showed that one SD increase in LVEF significantly correlated with decreased TSAT(β=-0.0699;95%CI:-0.1087 to-0.0311;P=0.0004).No heterogeneity or pleiotropic effects evidence was observed in the analysis.CONCLUSIONS We demonstrated a causal relationship between TSAT and LV remodeling and function in a preserved ejection fraction population.

Establishment of a chicken intestinal organoid culture system to assess deoxynivalenol‑induced damage of the intestinal barrier function

Background Deoxynivalenol(DON)is a mycotoxin that has received recognition worldwide because of its ability to cause growth delay,nutrient malabsorption,weight loss,emesis,and a reduction of feed intake in livestock.Since DON-contaminated feedstuff is absorbed in the gastrointestinal tract,we used chicken organoids to assess the DON-induced dysfunction of the small intestine.Results We established a culture system using chicken organoids and characterized the organoids at passages 1 and 10.We confirmed the mRNA expression levels of various cell markers in the organoids,such as KI67,leucine-rich repeat containing G protein-coupled receptor 5(Lgr5),mucin 2(MUC2),chromogranin A(CHGA),cytokeratin 19(CK19),lysozyme(LYZ),and microtubule-associated doublecortin-like kinase 1(DCLK1),and compared the results to those of the small intestine.Our results showed that the organoids displayed functional similarities in permeability compared to the small intestine.DON damaged the tight junctions of the organoids,which resulted in increased permeability.Conclusions Our organoid culture displayed topological,genetic,and functional similarities with the small intes-tine cells.Based on these similarities,we confirmed that DON causes small intestine dysfunction.Chicken organoids offer a practical model for the research of harmful substances.

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.In our research,we propose an optimization method to expedite density functional theory(DFT)calculations for systems with large aspect ratios,such as metallic nanorods,nanowires,or scanning tunneling microscope tips.This method focuses on employing basis set to expand the electron density,Coulomb potential,and exchange-correlation potential.By precomputing integrals and caching redundant results,this expansion streamlines the integration process,significantly accelerating DFT computations.As a case study,we have applied this optimization to metallic nanorod systems of various radii and lengths,obtaining corresponding ground-state electron densities and potentials.

Hyperbolic Tangent Function-Based Protocols for Global/Semi-Global Finite-Time Consensus of Multi-Agent Systems

This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.

Regulatory potential of soil available carbon,nitrogen,and functional genes on N_(2)O emissions in two upland plantation systems

Dynamic nitrification and denitrification processes are affected by changes in soil redox conditions,and they play a vital role in regulating soil N_(2)O emissions in rice-based cultivation.It is imperative to understand the influences of different upland crop planting systems on soil N_(2)O emissions.In this study,we focused on two representative rotation systems in Central China:rapeseed–rice(RR)and wheat–rice(WR).We examined the biotic and abiotic processes underlying the impacts of these upland plantings on soil N_(2)O emissions.The results revealed that during the rapeseed-cultivated seasons in the RR rotation system,the average N_(2)O emissions were 1.24±0.20 and 0.81±0.11 kg N ha^(–1)for the first and second seasons,respectively.These values were comparable to the N_(2)O emissions observed during the first and second wheat-cultivated seasons in the WR rotation system(0.98±0.25 and 0.70±0.04 kg N ha^(–1),respectively).This suggests that upland cultivation has minimal impacts on soil N_(2)O emissions in the two rotation systems.Strong positive correlations were found between N_(2)O fluxes and soil ammonium(NH_(4)^(+)),nitrate(NO_(3)^(–)),microbial biomass nitrogen(MBN),and the ratio of soil dissolved organic carbon(DOC)to NO_(3)^(–)in both RR and WR rotation systems.Moreover,the presence of the AOA-amoA and nirK genes were positively associated with soil N_(2)O fluxes in the RR and WR systems,respectively.This implies that these genes may have different potential roles in facilitating microbial N_(2)O production in various upland plantation models.By using a structural equation model,we found that soil moisture,mineral N,MBN,and the AOA-amoA gene accounted for over 50%of the effects on N_(2)O emissions in the RR rotation system.In the WR rotation system,soil moisture,mineral N,MBN,and the AOA-amoA and nirK genes had a combined impact of over 70%on N_(2)O emissions.These findings demonstrate the interactive effects of functional genes and soil factors,including soil physical characteristics,available carbon and nitrogen,and their ratio,on soil N_(2)O emissions during upland cultivation seasons under rice-upland rotations.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Risk-Balanced Routing Strategy for Service Function Chains of Cyber-Physical Power System Considering Cross-Space Cascading Failure

Cyber-physical power system(CPPS)has significantly improved the operational efficiency of power systems.However,cross-space cascading failures may occur due to the coupling characteristics,which poses a great threat to the safety and reliability of CPPS,and there is an acute need to reduce the probability of these failures.Towards this end,this paper first proposes a cascading failure index to identify and quantify the importance of different information in the same class of communication services.On this basis,a joint improved risk-balanced service function chain routing strategy(SFC-RS)is proposed,which is modeled as a robust optimization problem and solved by column-and-constraint generation(C-CG)algorithm.Compared with the traditional shortest-path routing algorithm,the superiority of SFC-RS is verified in the IEEE 30-bus system.The results demonstrate that SFC-RS effectively mitigates the risk associated with information transmission in the network,enhances information transmission accessibility,and effectively limits communication disruption from becoming the cause of cross-space cascading failures.

Winding Function Model-based Performance Evaluation of a PM Transverse Flux Generator for Applications in Direct-drive Systems

The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.

Effects of Repetitive TranscranialMagnetic Stimulation on Upper Extremity Function in Acute Stroke:A Meta-analysis and Systematic Review

[Objectives]To conduct a comprehensive examination of the evidence-based impact of repetitive transcranial magnetic stimulation(rTMS)on upper extremity functionality in patients with acute stroke.[Methods]A rigorous and systematic electronic search was conducted across the Medline,PubMed,and Web of Science databases,encompassing literature up to July 1,2024.To ensure the reliability of the in-cluded studies,an assessment of their risk of bias was conducted using RevMan 5.4 software,in accordance with the rigorous standards out-lined in the Cochrane Handbook for Systematic Revieus.Subsequently,we employed either the random-effects model or the fixed-effects model,depending on the heterogeneity of the data,to estimate the standardized mean difference(SMD)in outcomes,utilizing Stata 18.0 software for statistical analysis.[Results]Our review encompassed a total of five studies,involving 252 patients with acute stroke.The pooled analysis of these studies revealed a statistically significant improvement in Fugl-Meyer Assessment of the Upper Extremity(FMA-UE)scores among pa-tients who received rTMS therapy(SMD=2.71,95%CI:0.85 to 4.56;P<0.0001),albeit with considerable heterogeneity(I^(2)=97.65%)across the trials.[Conclusions]The results of this systematic review and meta-analysis underscore the promising potential of rTMS in enhancing upper extremity function in patients who have experienced an acute stroke.These findings provide compelling evidence for the therapeutic benefits of rTMS in this patient population.

Virtual Reality-Based Mirror Therapy for Upper Extremity Function among Stroke Patients:A Meta-analysis and Systematic Review

[Objectives]To investigate the evidence-based effect of virtual reality-based mirror therapy system(VR-MT)on upper extremity function among stroke patients.[Methods]A systematic electronic searching of the Medline,PubMed,Web of Science and CNKI was initially performed up to June 10,2024.The risk of bias of the included studies was evaluated using RevMan 5.4 software based on the Cochrane Handbook for Systematic Reviews.The random-effects model or fixed-effects models was employed to estimate the standardized mean difference(SMD).The subgroup analyses were conducted exploring theVR-MT type(immersive or non-immersive)and comparing with MT or control group.[Results]In total 8 studies with a total of 273 stroke patients were included in this review.The pooled analysis of these trials showed a statistically significant enhancement inFMA-UE scores(6 studies,SMD=0.72,[95%CI 0.37 to 1.06];P<0.0001,I^(2)=31%)and Box and Block Test(BBT)(3 studies,SMD=0.49,[95%C/0.05 to 0.93];P=0.03,I^(2)=0%),rather than Manual Function Test(MFT)scores(3 studies,SMD=0.38,[95%CI-0.09 to 0.84];P=0.11,I^(2)=0%)following the application of reality-based mirror therapy.Additionally,the subgroup analysis results indicated that immersive VR-MT can significantly improve FMA-UE(5studies,SMD=0.73,[95%CI 0.24 to 1.23];P=0.004,I^(2)=43%).In contrast,the overall effect of non-immersive VR-MT was non-significant(2 studies,SMD=0.33,[95%CI-0.69 to 1.34];P=0.53,I^(2)=72%).[Conclusions]In this systematic review and meta-analysis,our findings indicate that immersiveVR-MT has the potential to improve upper extremity function among stroke patients.