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The focus of this article is related to cognitive sciences: the problems of modeling neural networks and consciousness in general are discussed. Examples of the inadequacy of artificial intelligence systems based on neural network modeling are given, and problems of the modern numerical model of neural networks are considered. In order to solve these problems, the methodology of consciousness neuromodeling based on kinetic-statistical methods is proposed. It is shown that, in the process of quasi-chaotic complication of the neuro-like graph during the percolation transition, large structures (clusters) are formed, which can be interpreted as a manifestation of the primary elements of consciousness. The manifestation of the phenomenon of self-consciousness in the process of complication of the system of neural clusters is discussed. It is possible to use the results of this research for generation of complex neural networks with criteria of finite structure evaluation (number of cycles, simple paths, and Euler's number). [ABSTRACT FROM AUTHOR]

Like all raw materials of plant origin, persimmon fruits are considered a material rich in carbohydrates. This subtropical plant grows almost throughout the entire territory of the Republic of Azerbaijan. Despite the widespread distribution of this plant in the republic, very few types of products are produced from it. The main reason why persimmon fruits are not used effectively from a production point of view is that they have astringent properties. Since fruit carbohydrates play an important role in eliminating the tart taste of persimmons, the study of the carbohydrate complex was considered as a basic condition. After fractionation of carbohydrates with a water-alcohol mixture, certain stresses arise in the filter residue, which consists of cellulose-lignin. These stresses are analyzed using tensors. It has been established that the size of the filter pores is about 0.005÷0.05 microns, and the volume of these pores is 0.062÷0.195 cm³/g. The clearance coefficient averaged 19.97 %. It is known that the outer layer of a plant cell consists of cellulose and other structural compounds. These substances determine the porosity of the material. The mass fraction of the final product of the fractional residue, more precisely cellulose, averaged 0.63 %. The use of the resulting filter membrane in the clarification of fruit juices has shown its usefulness in industry. It has been established that the selectivity of these membranes for various amino acids is 5÷18 %, and for minerals 1÷30 %. The lipid resistance of the membranes was high. It should be noted that cellulose has the ability to restore its structure and at the last stage acts only as a filter membrane. This explains the usefulness of the celluloselignin mixture as a membrane material. [ABSTRACT FROM AUTHOR]

In this paper, we study how the influence of initiators (seeds) affects the tipping point of information cascades in networks. We consider an extended version of the Watts model, in which each node is either active (i.e., having adopted an innovation) or inactive. In this extended model, the adoption threshold, defined as the fraction of active neighbors required for an inactive node to become active, depends on whether the node is a seed neighbor (i.e., connected to one or more initiators) or an ordinary node (i.e., not connected to any initiators). Using the tree approximation on random graphs, we determine the tipping point, at which the fraction of active nodes in the final state increases discontinuously with an increasing seed fraction. The occurrence of a tipping point and the scale of cascades depend on two factors: whether a giant component of seed neighbors is formed when the seed fraction is large enough to trigger cascades among seed neighbors, and whether the giant component of ordinary nodes is maintained when newly activated nodes trigger further activations among ordinary nodes. The coexistence of two giant components suggests that a tipping point can appear twice. We present an example demonstrating the existence of two tipping points when there is a gap between the adoption thresholds of seed neighbors and ordinary nodes. Monte Carlo simulations clearly show that the first cascade, occurring at a small tipping point, occurs in the giant component of seed neighbors, while the second cascade, occurring at a larger tipping point, extends into the giant component of ordinary nodes. • The influence of seeds on tipping points is studied using an extended Watts model. • Cascade sizes for various thresholds of seed neighbors and ordinary nodes are shown. • The giant component sizes of seed neighbors and ordinary nodes are derived. • Two tipping points can appear when two giant components coexist. [ABSTRACT FROM AUTHOR]

The percolation transition behavior occurs in the solid-liquid separation of graphite oxide (GO), which changes the system from suspension to colloid state and terminates the separation process. An indicator of percolation transition is necessary to help control the status of GO suspension to finish the solid-liquid separation process. The swell ratio, macroscopic appearance TEM, and rheological behavior of GO suspension were tested before and after the percolation transition occurred in a specific interval of K+ concentration. Then, the physical properties of 1.00 g/L GO suspension containing 0.40–0.80 g/L K+, including conductivity, thermal conductivity, viscosity, surface tension, and absorbance were characterized. The values of these physical properties showed a sharp change in the specific interval of K+ concentration. We calculated the first and second slope of two adjacent points of each physical property to obtain a proper percolation transition indicator. The conductivity with the second slope up to 500% was the most significant change among these physical parameters, which can be used as an indicator of percolation transition in GO suspension. To verify the availability of the indicator, we explored the percolation transition behavior of Ca2+ and Al3+ in GO suspension and K+ with different GO solid content, found that the conductivity is still the most significant percolation transition indicator. The indicator obtained in this paper is reliable under varying content of GO and types of cations in suspension, which can be used to determine the percolation transition threshold during the solid-liquid separation of GO suspension containing cations. [ABSTRACT FROM AUTHOR]

We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erdőos-Rényi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems. [ABSTRACT FROM AUTHOR]

Steady increases in human population size and resource consumption are driving rampant agricultural expansion and intensification. Habitat loss caused by agriculture puts the integrity of ecosystems at risk and threatens the persistence of human societies that rely on ecosystem services. We develop a spatially explicit model describing the coupled dynamics of an agricultural landscape and human population size to assess the effect of different land‐use management strategies, defined by agricultural clustering and intensification, on the sustainability of the social‐ecological system. We show how agricultural expansion can cause natural habitats to undergo a percolation transition leading to abrupt habitat fragmentation that feedbacks on human's decision making, aggravating landscape degradation. We found that agricultural intensification to spare land from conversion is a successful strategy only in highly natural landscapes, and that clustering agricultural land is the most effective measure to preserve large connected natural fragments, prevent severe fragmentation and thus, enhance sustainability. [ABSTRACT FROM AUTHOR]

The paper deals with the specific electrical resistivity of liquid Fe–Mn alloys with the manganese content of 3.9, 6.0, 8.2, 10.3 and 13.2 at.%. A rotary-field electromagnetic method is used to measure this parameter. The experiments are conducted under heating conditions in the range from 1720 to 2070 K followed by the specimen cooling in pure helium. Most of alloys demonstrate a kink on the temperature curve of the specific electrical resistivity during heating up to 1900–2000 K. It is found that the specific electrical resistivity and the ratio between the conductivities of the liquid alloys and the inclusion grow with increasing manganese content in the alloy. Theoretical calculations are performed for the effective specific electrical resistivity of the liquid Fe–10 at.% Mn alloy in the temperature range 1720 to 2770 K. The certain temperature is determined, when the conductivity of the heterogeneous liquid alloy equals the conductivity of the iron solution in manganese with the uniform atom distribution. The obtained values of the certain temperature range between 2050– 2100 K, i.e., are higher than 1900–2000 K, at which the kink appears on the temperature curve of the electrical resistivity. Theoretical studies are presented for the percolation transition in heterogeneous liquid Fe–Mn alloys. The limit value is identified for the ratio between the electrical resistivity of liquid alloys and the inclusion, when a percolation transition is possible. The percolation threshold is determined as a volume fraction of inclusions, at which the effective specific electrical resistivity significantly reduces. The latter is calculated for the heterogeneous liquid alloy in the Maxwell approximation (interpreted by А. А. Snarskii). [ABSTRACT FROM AUTHOR]

Natural porous media possess spatial heterogeneous (fractional) wettability, which controls the multiphase flow behavior, that is, displacement and trapping. We used mixed hydrophilic (contact angle θ = 0°) and hydrophobic (θ = 100°) 1 mm sands and 1 mm glass beads as model systems for fractional wet porous media. Both porous media have the same morphological characteristics (Minkowski functions). A comparative μ‐CT study of such fractional wet systems is lacking in the literature. A previous study (Geistlinger & Zulfiqar, 2020, https://doi.org/10.1029/2019wr026826) showed a percolation transition of the invading fluid from compact to fractal displacement when the wettability changed from imbibition to drainage. This correlates to a transition from no to maximal trapping. For the first time, we observed in fractional wet glass bead packs, a second structural percolation transition with a percolation threshold of approximately 50% hydrophobic glass beads. Below this threshold, the percolating cluster consisted of hydrophilic glass beads, which resulted in compact displacement without any trapping. Above the threshold, the percolating cluster consisted of hydrophobic glass beads, which resulted in fractal displacement with maximal trapping. Trapping occurred only in hydrophobic environments/configurations, that is, when the trapped clusters were surrounded by hydrophobic glass beads. Fractional wet glass beads and sands show an opposite trapping behavior, that is, the trapping efficiency increases for glass beads, whereas it decreases for sands with increasing percentage of hydrophobic grains. Interestingly, the trapping efficiency approaches the same limit value for pure hydrophobic sands and glass beads. This demonstrates that bypass trapping is the dominant trapping mechanism, because it depends strongly on the pore connectivity. Key Points: Fractional wet glass beads and sands with same morphological properties (pore space connectivity) show an opposite trapping behaviorPure hydrophobic sands and glass beads show equal trapping efficiency caused by bypass trapping (equal pore space connectivity)Structural (site) percolation transition with a percolation threshold of approximately 50% hydrophobic glass beads [ABSTRACT FROM AUTHOR]

Upon placement of an implant into living bone, an interface is formed through which various biochemical, biological, physical, and mechanical interactions take place. This interface evolves over time as the mechanical properties of peri-implant bone increase. Owing to the multifactorial nature of interfacial processes, it is challenging to devise a comprehensive model for predicting the mechanical behavior of the bone-implant interface. We propose a simple spatio-temporally evolving mechanical model – from an elementary unit cell comprising randomly oriented mineralized collagen fibrils having randomly assigned stiffness all the way up to a macroscopic bone-implant interface in a gap healing scenario. Each unit cell has an assigned Young's modulus value between 1.62 GPa and 25.73 GPa corresponding to minimum (i.e., 0) and maximum (i.e., 0.4) limits of mineral volume fraction, respectively, in the overlap region of the mineralized collagen fibril. Gap closure and subsequent stiffening are modeled to reflect the two main directions of peri-implant bone formation, i.e., contact osteogenesis and distance osteogenesis. The linear elastic stochastic finite element model reveals highly nonlinear temporal evolution of bone-implant interface stiffness, strongly dictated by the specific kinetics of contact osteogenesis and distance osteogenesis. The bone-implant interface possesses a small stiffness until gap closure, which subsequently evolves into a much higher stiffness, and this transition is reminiscent of a percolation transition whose threshold corresponds to gap closure. The model presented here, albeit preliminary, can be incorporated into future calculations of the bone-implant system where the interface is well-defined mechanically. A simple, physically informed model for the mechanical characteristics of the bone-implant interface is still missing. Here, we start by extending the reported mechanical characteristics of a one cubic micrometre unit cell to a 250 µm long interface made of 1 µm thick layers. The stiffness of each cell (based on mineral content) is assigned randomly to mimic bone micro-heterogeneity. The numerical study of this interface representative structure allows for the simultaneous determination of the spatio-temporal evolution of the mechanical response at local (discrete element) and global (overall model) scales. The proposed model is the first of this kind that can easily be incorporated into realistic future models of bone-implant interaction with emphasis on implant stability and different loading conditions. [Display omitted] [ABSTRACT FROM AUTHOR]

It is proposed that the O (n) spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed. [ABSTRACT FROM AUTHOR]

We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erdőos-Rényi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems.

Fluid invasion, displacement of one fluid by another in porous media, is important in a large number of industrial and natural processes. Of special interest is the trapping of gas and oil clusters. We study the impact of wettability on fluid pattern formation and capillary trapping in three‐dimensional glass beads packs (dmean = 1 mm) during fluid invasion at capillary numbers of 10−7 using μ‐CT. The invading fluid was water, and the defending fluid was air. The contact angle of the glass beads was altered between 5° and 115° using Piranha cleaning and silanization. We analyzed the front morphology of the invading fluid, the residual gas saturation, the fluid occupation frequency of pores, and the morphology and statistics of the trapped gas clusters. We found a sharp transition (crossover) at a critical contact angle θc = 96°. Below θc the morphology of the displacement front was flat and compact caused by the strong smoothing effect of cooperative filling. Above θc the morphology of the displacement front was fractal and ramified caused by single bursts (Haines jumps). Across this dynamical phase transition the trapping efficiency changes from no trapping to maximal trapping. For θ > θc the experimental results show that invasion percolation governs the fluid displacement. Strong indicators are the universal scaling behavior of the size distribution of large clusters (relative data error εdata < 1%) and their linear surface‐volume relationship (R2 = 0.99). Key Points: Wettability‐controlled dynamical phase transition in trapping efficiency for 3‐D porous media (1‐mm glass beads)Trapping efficiency changes from no trapping to maximal trapping: Above the critical contact angle θc smaller pores are occupied by gasFor θ > θc the results show that invasion percolation governs the fluid displacement: universal scaling for the trapped gas clusters [ABSTRACT FROM AUTHOR]

Nanocarbon composites present a new type of nanomaterials consisted of electric conducting carbon nanoparticles and a non-conducting matrix. A typical example of such composites is a polymer matrix doped with carbon nanotubes (CNT). Due to a high aspect ratio of nanotubes insertion of very small quantity of CNT (on the level of 0.01%) promotes the percolation transition resulting in an enhancement of the conductivity of the material by 10–12 orders of magnitude. Another type of nanocarbon composite is a film consisted of partially reduced graphene oxide (GO) produced as a result of thermal reduction of graphite oxide material. Distinctive peculiarity of both types of nanocomposites relates to the dependence of the specific resistivity of the materials on the applied voltage. Such a behavior is caused by non-ideal contacts between neighboring carbon particles involving into the composite. The resistance of this contact depends drastically on the intra-contact field, which promotes the dependence of the material resistivity on the applied voltage. The model description of such a non-linear dependence has been presented. The calculation results are compared with both literature data and the measured data obtained for reduced GO thermally treated at various temperatures. [ABSTRACT FROM AUTHOR]

Metallic microparticles, suspended in a dielectric liquid in external alternating electric field, tend to organise into regular structures. Since the structures depend on the external field parameters, they enable testing the general properties of complex systems, as well as engineering new (meta)materials. In our experiments on Cu microparticles suspended in a mixture of rapeseed oil and n-hexadecane in AC field, four system states (structure types) were distinguished and described: (i) driven gas state, (ii) vertical chains, (iii) fully randomly oriented chains, and (iv) percolation state. The states can be rapidly switched by manipulating the amplitude and the frequency of the AC field. The states exhibiting higher and lower order occur alternatingly versus a one-field-parameter scan. Two interstate transitions, involving microstructure reorganisation, were discussed in detail: (1) driven gas-vertical chains state transition and (2) randomly oriented chains-percolation state transition. A simple model of interactions, utilising the concept of a local electric field and considering charges and dipoles interactions, was proposed to explain the driven gas-vertical chains state transition. The transition was found independent of the external field amplitude, and the transition frequency was found to be only on dependent material properties. A simple formula predicting the transition frequency was obtained. The randomly oriented chains/percolation network transition was discussed in detail. The transition position for external field frequency and amplitude was found unequivocal, though a significant formation/disintegration hysteresis was observed versus both these parameters. The transition was found to be weakly dependent on the microparticle charge and the network formation is expected to be controlled by ohmic current. Thus, a description in the language of electric circuits was proposed for future development. [ABSTRACT FROM AUTHOR]

There are many target methods that are efficient to tackle the robustness and immunization problem, in particular, to identify the most influential nodes in a certain complex network. Unfortunately, owing to the diversity of networks, none of them could be accounted as a universal approach that works well in a wide variety of networks. Hence, in this paper, from a percolation perspective, we connect the immunization and robustness problem with an evolutionary algorithm, i.e., a framework of an evolutionary algorithm for investigation of influential nodes in complex networks, in which we have developed procedures of selection, mutation, and initialization of population as well as maintaining the diversity of population. To validate the performance of the proposed framework, we conduct intensive experiments on a large number of networks and compare it to several state-of-the-art strategies. The results demonstrate that the proposed method has significant advantages over others, especially on empirical networks in most of which our method has over 10% advantages of both optimal immunization threshold and average giant fraction, even against the most excellent existing strategies. Additionally, our discussion reveals that there might be better solutions with various initial methods. [ABSTRACT FROM AUTHOR]

Topologically disordered films based on binary mixtures of SiO2 nanoparticles with CdS quantum dots on their surface with different surface and volume concentrations are studied. For the first time, a percolation transition of excitons has been observed in the CdS quantum dots array on a quasi-two-dimensional surface and the features of its formation have been described qualitatively. A percolation transition of excitons in a fi lm based on a binary mixture of pure SiO2 spheres and those coated with quantum dots (SiO2/CdS), which is analogous to the phase transition of metal and dielectric macroparticles, has also been observed. It is shown that the percolation transition in such a system occurs at a critical concentration of nanoparticles of one sort (nc ~ 0.6), which is almost twice as high as in the macroparticle system (~0.29). This is due to the interaction between nanoparticles (van der Waals forces and electrostatic forces) and the chemical nature of the binding ligand. [ABSTRACT FROM AUTHOR]

The metallic glass (MG) exhibits composition fluctuation or chemical heterogeneity during relaxation. However, the influence of this factor on the evolution of the intrinsic structural heterogeneity of MGs remains unclear. In this study, we systematically examined the co-evolution between atomic and nano-scale structural heterogeneities of Fe-Si-B-Cu MGs during relaxation. We discovered that, despite some degree of fluctuation in composition during the relaxation of Fe-Si-B-Cu MGs, it does not prevent the reduction of structural heterogeneities at the atomic/nano scale. The results demonstrate an overall increase in the number density and number of types of densely packed clusters with a high degree of local five-fold symmetry and a decrease in the number density and number of types of loosely packed clusters with a low degree of local five-fold symmetry. Furthermore, a certain degree of compositional fluctuation during relaxation of Fe-Si-B-Cu MGs facilitates the formation of uniformly distributed Fe-rich regions and Cu-rich regions. [ABSTRACT FROM AUTHOR]

Percolation transition is an important scientific question for characterizing complex two-phase flow phenomena in fractional-wet porous media composed of different wetting grains. Recent studies have shown significant transitions of fluid distribution and pressure system in fractional-wet porous media by changing wettability proportion. However, very few studies have systematically investigated controlling factors of percolation transition in spontaneous imbibition. Additionally, there is a lack of comprehensive knowledge and experimental observations about imbibition recovery and dynamic imbibition phenomena (including imbibition time, imbibition rate, and induction time) in fractional-wet porous media. In this study, these knowledge gaps are filled through a series of water imbibition experiments for fractional-wet artificial porous media with different water-wet proportions, three pore diameters, and two wettability heterogeneities. The results show that pore diameter and wettability heterogeneity are influential factors for percolation transition. Decreasing water-wet proportion results in the emergence of induction time, as well as the absences of transition and late imbibition stage, small pore radius enhances these negative impacts. Under strong wettability heterogeneity, relationship of water-wet proportion and imbibition recovery follows the classical percolation theory containing two percolation transitions. Small pore diameter retards percolation transitions, and weakens fluid displacements of the transition stage and late stage in the partial imbibition. Moreover, effects of water-wet proportion on dynamic imbibition phenomena exhibit exponential relationship resulted from transition of pathway type. Additionally, through decreasing wettability heterogeneity, three percolation transitions and an optimal imbibition ability are achieved, thus hydrophilization of hydrophobic pore is advantageous for water imbibition. These intriguing findings can broaden current knowledge about spontaneous imbibition in fractional-wet porous media. [Display omitted] [ABSTRACT FROM AUTHOR]

The transition from a semiconductor to a fast-ion conductor with increasing silver content along the Agx(Ge0.25Se0.75)(100−x) tie line (0≤x≤25) was investigated on multiple length scales by employing a combination of electric force microscopy, X-ray diffraction, and neutron diffraction. The microscopy results show separation into silver-rich and silver-poor phases, where the Ag-rich phase percolates at the onset of fast-ion conductivity. The method of neutron diffraction with Ag isotope substitution was applied to the x=5 and x=25 compositions, and the results indicate an evolution in structure of the Ag-rich phase with change of composition. The Ag–Se nearest-neighbours are distributed about a distance of 2.64(1) Å, and the Ag–Se coordination number increases from 2.6(3) at x=5 to 3.3(2) at x=25. For x=25, the measured Ag–Ag partial pair-distribution function gives 1.9(2) Ag–Ag nearest-neighbours at a distance of 3.02(2) Å. The results show breakage of Se–Se homopolar bonds as silver is added to the Ge0.25Se0.75 base glass, and the limit of glass-formation at x≃28 coincides with an elimination of these bonds. A model is proposed for tracking the breakage of Se–Se homopolar bonds as silver is added to the base glass.

Present work reports the formation of different types of alcohol-free emulsions consisting of TX-100 (surfactant), oleic acid (oil phase) and water. The phase behavior of ternary system (water/oleic acid/TX-100) was observed which showed single phase, multiphase and gel phase regions. The prepared emulsions with a wide range of composition were thermodynamically stable. Investigations into the stability of emulsions under milder conditions showed that they remained stable over four months and even at high centrifugation. A progressive transformation of the water-in-oil (w/o) to bicontinuous phase and inversion to oil-in-water (o/w) microemulsions occurred upon dilution with water, which was confirmed by electrical conductivity, viscosity and microscopic measurements. A static percolation phenomenon was observed in the investigated alcohol-free-emulsion system and the water content at percolation threshold was determined. [ABSTRACT FROM AUTHOR]

This study reviews the structure and properties of nanostructured composite conductometric sensors based on semiconducting metal oxides, and the physico-chemical processes occurring when applied for detection of ambient reducing gases. It discusses the mechanisms of electronic and chemical sensitization in composites comprised of metal oxides of different electronic and chemical properties. In particular, the relationship between the conductivity mechanisms and sensory effect is examined, considering the transfer of electrons between the oxide components of the composite semiconductor sensor. A separate section is devoted to new systems consisting of composite nanofibers of the core-shell type, the sensory characteristics of which depend on the transfer of electrons between the core and the shell in the nanofiber. It is demonstrated that by changing the nature of the components and their relative locations in such nanofibers, the sensitivity and selectivity of the sensor system can be tailored to various chemical compounds. Thus, the use of composite metal oxide systems can lead to improved efficiency and selectivity of conductometric sensors, and enable the development of sensor systems with the desired operating properties. [ABSTRACT FROM AUTHOR]

Metallic glasses are structurally heterogeneous on the atomic and nano scales. However, few investigations have been conducted on how the structural heterogeneities in these two scales co-evolve during annealing. In this work, the atomic and nanoscale structural heterogeneity evolution accompanying the magnetic softness is systematically discussed based on the literature and our previous synchrotron X-ray diffraction and atomic force microscopy results. We revealed the co-evolution mechanism of structural heterogeneities on the atomic and nano scales during annealing via the insight of percolation theory from the point of view of the local five-fold symmetry of the clusters. The results indicate that the reduction of atomic-scale structural heterogeneity during annealing is accompanied by an increase in the degree of local five-fold symmetry of the clusters and an alteration in their connection patterns. As the local five-fold symmetry of clusters in Fe-based metallic glasses reaches the percolation threshold, the nanoscale liquid-like regions tend to transform into solid-like regions. The great degree of percolation causes the pronounced weakening of the nanoscale structural heterogeneity accompanying changes in the shape and number of the liquid-like regions. The reduction of the number of liquid-like regions causes a reduction in vertical anisotropy and magnetic softening due to a more uniform and less free volume within the sub-circular shaped liquid-like region. • The evolution of the atomic/nano scale structural heterogeneity and its relation to the magnetic softness was discussed • The co-evolution mechanism of structural heterogeneities on the atomic and nano scales during relaxation is revealed. • The shape of liquid-like regions tend to become nearly circular during relaxation contributing to magnetic softening. [ABSTRACT FROM AUTHOR]

The problem of finding a better immunization strategy for controlling the spreading of the epidemic with limited resources has attracted much attention since its great theoretical significance and wide application. In this letter, we propose a novel and successful targeted immunization strategy based on percolation transition. Our strategy repeatedly looks for the critical nodes for immunizing. The critical node, which leads to the emergence of the giant connected component as the degree threshold increases, is determined when the maximal second-largest connected component disappears. To test the effectiveness of the proposed method, we conduct the experiments on several artificial networks and real-world networks. The results show that the proposed method outperforms the degree centrality strategy, the betweenness centrality strategy and the adaptive degree centrality strategy with 18% to 50% fewer immunized nodes for same amount of immunization. [ABSTRACT FROM AUTHOR]