Here we show such interplays in a Ag55 nanocluster using real-time time-dependent density functional theory simulations. We find that the disappearance of the zero-frequency peak in the Fourier transform of the band-to-band transition coefficient is a hallmark of the plasmon. We show the importance of the d-states for hot-carrier generations. If the single-particle d-to-s excitations are resonant to the plasmon frequency, the majority of the plasmon energy will be converted into hot carriers, and the overall hot-carrier generation is enhanced by the plasmon; if such resonance does not exist, we observe an intriguing Rabi oscillation between the plasmon and hot carriers. Phonons play a minor role in plasmonic dynamics in such small systems. This study provides guidance on improving plasmonic applications.Plasmon-generated hot carriers are used in photovoltaic or photochemical applications. However, the interplays between the plasmon and single-particle excitations in nanosystems have not been theoretically addressed using  Plasmons can enhance hot-carrier generation for efficient photochemical reactions, but the interplay between plasmons and single-particle excitations are difficult to capture in models. Here, the authors use real-time time-dependent density functional theory to study these interactions in silver nanocrystals. Plasmons are collective oscillations of the electron density, which can convert light energies into electronic excitations1346189101112131415ω of the inverse dielectric function ɛ−1ν satisfies ∫ɛνdr2=0. Here the plasmon frequency ωp is a complex number, with its imaginary part indicating the plasmon life time. Unfortunately ɛ−1 does not provide a real-time picture of the interplays between the plasmon and hot carriers. There are several recent theoretical studies on the plasmon-induced hot-carriers generations, showing that hot carriers can be effectively excited by plasmons24Plasmon modes can be simulated classically using the Drude model and Maxwell equations. Such calculations can yield accurate plasmon modes for systems down to tens of nanometres. However, when the system sizes shrink to the order of nanometres, the classical method could fail1717192021The real-time (rt) time-dependent density functional theory (TDDFT) is a powerful tool to study the plasmonic processes. The rt-TDDFT describes directly the Coulomb interactions between electrons, and its ability to describe plasmons has been demonstrated in many previous publications262728292627282855 nanocluster. The Ag55 nanocluster has been experimentally synthesized and its atomic structure is well determined32d-to-s excitations resonant to the plasmon frequency exist, most plasmon energy will be converted into hot carriers, enhancing hot-carrier generations. However, if the resonances do not exist, the plasmon decays slowly and may exhibit Rabi oscillations. We propose that by modifying the electronic structures of nanoclusters , the plasmon decay and hot-carrier generations can be tuned. The electron–phonon interactions play a minor role during the plasmon decay in Ag55.In this work, we will use rt-TDDFT to study the plasmon dynamics in a Ag55 are shown in 55 has 605 electrons and is an open-shell system. The 301st–303rd states are almost degenerated and partially occupied, and the 304th state is the lowest unoccupied state (LUMO). To study the excitations, we apply an external electric field ωl with a Gaussian envelope. The optical absorption spectrum can be obtained from the time-dependent dipole response (the imaginary part of α(ω) described in Methods section), and is shown in ωp≈3.6 eV, which is in good agreement with the recent experimental result of 3.8 eV =ρ−ρ0(r) (where ρ0(r) is the ground-state charge density) at t=19.2 and 19.8 fs are shown in ρ is localized on the surface, and sloshes from one side of the nanocluster to the other, fitting well with the classical picture of the surface plasmon. From 20 to 27 fs, the dipole oscillation amplitude decays to relatively small values. Two of the charge density differences Δρ at t=38.0 and 38.6 fs are shown in ρ is not localized on the surface and does not slosh, which may suggest the plasmon decay qualitatively. Such dipole oscillations can be observed experimentally as demonstrated in a recent experiment by Mittal et al.To exam the resonant excitation, we set the laser frequency ωp overlaps with the single-particle excitation energies, which makes their interplays interesting but difficult to analyse. There are several previous publications on this topic using different approaches1123373839404142ith eigen state to the jth eigen state also produces a charge density oscillation. This can be seen from the expansion of the time-dependent wave function ψi(t) on the eigen states in a perturbation theory:How to distinguish the collective plasmon excitation from the non-collective single-particle excitation quantum mechanically is a challenging issue. In particular, for small molecules and nanostructures, the plasmon frequency and the charge density change isωj,i=ωj−ωi=ωp, so Δρ(t) also oscillates at the frequency ωp. Thus, we cannot use the charge density (or dipole moment) oscillation alone to tell the difference. One can attempt to use the charge density plot, such as et al.Cj,i(t), especially the Fourier transform of Cj,i(t) , compared with Cj,i(t) of single-particle excitations. In the following we will take j=304 (LUMO) state as an example to discuss the behaviours of Cj,i(t). i≤303) to the LUMO state (the 304th state). We observe two clearly distinct types of transitions. One type of i=292), and the other shows smooth amplitude variations .ωLUMO−ωi≈ωp . The Fourier transform of CLUMO,253(t) =f(t), where f(t) is a slowly varying (compared with ωp) function, and All the slowly varying transitions have nearly resonant energies O,253(t)  shows onωj,i≈ωp can be effectively excited. The charge density oscillates at Δωj,i≈ωp due to the phase factor exp. The single-particle excitations correspond to the so-called ‘hot-carriers'.This is a typical independent single-particle excitation described by the single-particle time-dependent perturbation theory within the rotating-frame approximation. Only single-particle transitions with nearly resonant frequencies ΔωLUMO−ωi<ωp , and the Fourier transform of CLUMO,292(t) shows two peaks at Δωj,i±ωp. Both the real and imaginary parts of CLUMO,292(t) =A exp[it]+B exp[it], and it can be written as A, B and f(t) are slowly varying (compared with ωp) functions, and θ is a complex phase factor. Thus, In contrast, all the rapidly oscillating transitions have off-resonant energies O,292(t)  oscillatωj,i≈ωp, as Δωj,i does not appear in ωp. These synchronized off-resonant transitions constitute the plasmon mode. Since there is no resonant requirement for the plasmon-related transitions, many transitions with i to j transitions are reduced. In It cannot be described by the single-particle perturbation theory. It also does not require that the resonant condition ΔCj,i(t) comes from the plasmon, we have performed a time-dependent evolution on a non-interacting system with the same external electric field. In this simulation, we fix the potential in the Hamiltonian V=V  making it independent of the charge density. We would like to stress that this non-interacting system is an unrealistic system with no experimental counterpart. In this model, all the electrons are treated as independent single particles. Because the electron–electron interaction is zero, the plasmon excitation is impossible. Thus, the plasmon-related transitions should behave differently, while the single-particle transitions should remain the same.To further prove that the rapidly oscillating i=253), both the i=292) are replaced by irregular oscillations. The irregularly oscillating transitions decay with time, and almost disappear after the laser fades off. Besides the two peaks at Δωi,j±ωp in CLUMO,292(t) has a strong peak at ω=0 in ωpt) perturbation along the x axis:The dipole moment of the non-interacting system inset of  shows anoth the   and the oth the   are simiωp, there are extra oscillating terms at the frequencies Δωj,i. These off-resonant oscillations have different Δωj,i and thus cannot add up in sync, which results in the irregular oscillations shown in ω=0 peak in the Fourier transform must disappear, which is a hallmark of the plasmon mode. The disappearance can only exist with interactions between different transitions.Apparently, the Fourier transform should have three peaks in agreement with those in λ=0 in ref. χ equals to that of the non-interacting system χ0. Thus, their model system with no electron–electron interactions is exactly the same as our non-interacting system. The absorption spectrum of the non-interacting system is exactly the DFT result shown in λ increases. Similarly, we find that the main absorption peak of the real system (λ=1) is ∼1.9 eV higher than that of the non-interacting system (λ=0).In refs i=253 and 292 with j=LUMO to represent the two types of transitions, respectively. All other transitions can also be classified into the two distinct types. The In the discussion above, we have used Cj,i(t) due to the electron–electron interaction is a hallmark of the plasmon. For single-particle excitations, the charge density oscillation comes from the phase factor interference between φi and φj  and Cj,i(t) does not oscillate; for plasmons the oscillation comes from the Cj,i(t) amplitude oscillations. Each transition  can either belong to plasmon (off-resonant) or single-particle (near-resonant), but cannot belong to both. This provides an unambiguous way to sort out the plasmon from single-particle excitations.Here we summarize the analysis above. Both the plasmon and single-particle excitations are described by band to band transitions  in TDDFTj and i denote unoccupied and occupied states, respectively), which represents the number of transitions at the energy ω for a given time t. For the real system, as shown in SC has peaks around 1.5–2.5 eV at t=17 fs. Those off-resonant transitions constitute the plasmon. At t=39 fs, those off-resonant peaks disappear, and the resonant peak is strengthened, showing that the plasmon has been converted into resonant single-particle excitations (hot carriers). From t=17 to 39 fs, the laser is off. Thus, the hot carriers are generated completely by the plasmon. For the non-interacting system  shows much smaller peaks around 1.5–2.5 eV (no plasmons), while the main peak always appears at the resonant frequency (single-particle excitations). There is no change in SC from 17 to 39 fs because there are no laser nor electron–electron interactions.We have calculated the energy spectrum of g system , SC defined by jth eigen state. The numbers of excited electrons (positive ΔOj(t)) on all eigen states are shown in j can have both resonant and off-resonant transitions from different states i, ΔOj(t) is a combination of both slowly varying and rapidly oscillating components as shown in Cj,i(t) in d-states to the eigen states around the Fermi energy are the major plasmon decay (hot-carrier generation) channels.We have also calculated Δt=0, the light energy is absorbed by both the plasmon and resonant single-particle (hot-carrier) excitations, with almost equal rates. Compared with the non-interacting system, the single-particle energy of the real system is lower at first (the blue line is negative), indicating that less hot carriers are generated at first due to the plasmon. After 3 fs, the blue line becomes positive, indicating more hot carriers are generated due to the plasmon. After the laser fades off at t=10 fs, the energy in the plasmon mode does not decay immediately, and we even observe a small single-particle to plasmon energy transfer around t=17 fs. From 20 to 30 fs, the plasmon energy starts to decay and is almost completely transferred into single-particle excitations. The speed of the decay agrees with previous experiments that the plasmon decay timescale is 1–100 fs (refs ωpt/Q), we obtain Q=13.3 , as shown in  fs refs , 36. By t=8 and 30 fs are shown in t=8 fs, there are broad excitations around the Fermi energy, indicating the plasmon excitation. At t=30 fs, as the plasmon is decayed to hot carriers, the excited electrons and holes are concentrated in a few sharp peaks. These peaks can be classified into two groups. The major hot holes are around −3.6 eV with the corresponding electrons around the Fermi energy (d to s transitions). There are fewer hot holes at −1.1 eV with the corresponding hot electrons at 2.5 eV (s to p transitions). In a recent perturbation calculation of plasmon-induced hot-carriers in bulk Ag . It is interesting to see what would occur if these transitions are blocked. We first consider the negatively charged j≤303 are fully occupied, and thus cannot accept electrons from d-states. The only important channel is the d to 304th state excitation. The amplitude of the dipole oscillation of 55 (Oj(t)  channels are blocked in As mentioned above, the major hot-carrier generations in Agtion of   decays m of  (55 . The num5 (Oj(t)  confirm 5 (Oj(t) . After 15 (Oj(t) . The chaOj(t) . To change the system more dramatically, one may change the plasmon or single-particle frequencies. Experimentally, it can be realized by alloying with other metals, changing the nanocluster size/shape, or using some dielectric mediums. Theoretically, by further modifying the pseudopotential (see Methods section), we can artificially push down the d-state energies, making the d to s transition energies much greater than the plasmon frequency. Thus, all the single-particle d to s excitations become impossible. First, we observe an intriguing oscillation of the dipole amplitude (Oj(t) (s to p excitations). However, their transition energies are slightly off-resonant from the plasmon frequency by ∼0.2 eV, and ΔOj exhibits Rabi oscillations at the frequency Δωj,i−ωp. We also observe a cyclic energy transfer between the plasmon and single-particle excitations at the Rabi frequency (ρ (t=19.2 and 19.8 fs (more energy is stored in the plasmon) show stronger charge localization on the surface than those at t=41.4 and 42.0 fs (more energy is stored in the hot carriers). Around 40 fs, there is still charge localized on surface, because the plasmon is not fully decayed. Although Rabi oscillations in two-level systems are well known, it is interesting to observe Rabi oscillations between a collective plasmon mode and individual hot carriers. In the original Ag55  e (Oj(t)  still shrequency . Differeences Δρ  at t=19.nal Ag55 , we alsoet al.ab initio forces in the rt-TDDFT, and are able to describe the electron–phonon effects explicitly. The results for neutral Ag55 and Ag55 without resonant hot-carrier generation channels are shown in The simulations above have only included plasmon dampings through hot-carrier generations within TDDFT. We have not included the electromagnetic radiation. 55 nanocluster. Our rt-TDDFT simulations include the electron–electron interactions and electron–phonon interactions (using the Ehrenfest dynamics). The plane-wave basis set allows accurate descriptions of excited states. We do not include the electromagnetic radiations because they are extremely small in Ag nanoclusters. The simulations are under DFT and Kohn-Sham orbital framework, and do not explicitly use many-body wave functions. We propose an approach to distinguish the plasmon from single-particle excitations based on band to band transition coefficients Cj,i(t). We find that the collective plasmon consists of off-resonant transitions with Cj,i(t) oscillating in their amplitudes at the plasmon frequency, whereas the single-particle excitation is characterized by a slowly varying Cj,i(t). The disappearance of the ω=0 peak in the Fourier transform of Cj,i(t) makes the plasmon-related transitions different from the conventional independent off-resonant transitions described by the single-particle time-dependent perturbation theory, and is a hallmark of the plasmon. In Ag55, the single-particle d to s excitations resonant to the plasmon frequency exist. The plasmon will decay and generate hot carriers, and significantly enhance the hot-carrier generation rates. The main hot-carrier generations are from the low-energy d-states to the s-states around the Fermi energy. When applying a high-intensity laser, we also observe some nonlinear high-energy excitations. When most hot-carrier generation channels are blocked in d to s excitations have been completely blocked. Our rt-TDDFT Ehrenfest dynamic simulations show that the electron–phonon interactions do not play important roles in the plasmon decay in nanoclusters.We have performed rt-TDDFT simulations on the Agd10 and 5s) are expanded using plane-waves with an energy cutoff of 40 Ry. Although the plane-wave basis set significantly increases the computational cost compared with the local orbital basis set, it can describe the high-energy excited states and charge responses more accurately, which is critical for the plasmon study. The Brillouin zone integration is sampled with the Γ point only for the isolated Ag55 cluster. DFT cannot correctly predict the energies of the Ag d-states, which may affect the accuracy of the plasmon calculations28d-states, we add a Gaussian term to the d-channel of the Ag pseudopotential. We have fitted the pseudopotential so that the calculated density of states of the Ag d-bands agrees well with the experimental X-ray photoemission spectroscopy dataOur fast rt-TDDFT algorithm55 adopts the icosahedral structure3255, and the simulated time-dependent results have similar features to those of the icosahedral structure, as shown in 55, which is shown in In experiments, the Ag55 nanocluster, and treat the Ag 4d electrons as valence electrons. Thus, our simulations give more accurate descriptions of the system than the studies based on jellium models.In our simulations, we explicitly consider the atomic structure of the AgSC, we broaden the Dirac δ function using a Gaussian function with a s.d. of 0.1 eV.When calculating the density of states, the DFT absorption spectrum, and 55 in experiments due to the high mobility of the nanoclusterThe rt-TDDFT simulation explicitly includes the electron–electron interaction, which is critical for the plasmon excitation and plasmon-induced hot-carrier generations. The rt-TDDFT does not include the radiative damping. Previous study shows that the radiative effect is very weak for small Ag nanoclusters, so it is safe to ignore itψi(t) at t=0 is occupied according to the ground-state Fermi-Dirac occupation number ψi(t) are always orthogonal to each other. To evolve ψi(t) with time, we expand it onto the adiabatic eigen states φj(t) (which satisfies Hφj(t)=ωj(t)φj(t) for the time-dependent Hamiltonian H):In our rt-TDDFT simulations, the time-dependent electronic state Cj,i is the expansion coefficient which can be calculated using our rt-TDDFT algorithmCj,i (i≠j) represents the transition from the ith adiabatic eigen state to the jth adiabatic eigen state. We note that Cj,i might depend on an arbitrary phase factor due to the non-unique definition from φj(t) to φj(t+dt). We have removed this arbitrary phase factor by requiring φj(t) can be taken as a real function (without magnetic fields), there will be no Berry phase. The simulation is under DFT and Kohn-Sham orbital framework, and thus it does not explicitly use many-body wave functions. By using our new algorithm, we can set the simulation time step to 0.1 fs ωj for the purpose of analysis, as the variations of ωj(t) are rather small.The The charge density is calculated byCj,i, we define the occupation change ΔOj(t) on the jth adiabatic eigen state as:Using the coefficients Oj(t) represents the occupation change on the jth adiabatic eigen state at time t with respect to its ground-state occupation Oj(t) can be either positive or negative. Positive ΔOj(t) indicates increasing occupations (excited electrons) and negative ΔOj(t) indicates decreasing occupations (excited holes).The ΔTo simulate the laser excitations, we apply an external electric field to the Hamiltonian to mimic the laser pulseE is along the x axis. σ, ωl and ωl=ωp=3.6 eV, σ=6 fs and The electric field The polarizability can be obtained from the time-dependent dipole moment of the nanocluster51D(ω) and E(ω) are the Fourier transforms of the dipole moment and the electric field, respectively. The absorption spectrum is obtained from the imaginary part of α(ω).where The energies stored in the plasmon and the single-particle (hot-carrier) modes are estimated asj, i)∈plasmon' and ‘∈single' indicate the Cj,i(t) belongs to the rapidly oscillating transitions and the slowly varying transitions, respectively. For a given  pair, the Cj,i(t) either belongs to the plasmon or single particle, and there is no mixture between the two types. Thus the energies in where ‘.Supplementary Figures 1-6, Supplementary Notes 1-5 and Supplementary References


Much empirical evidence shows that individuals usually exhibit significant homophily in social networks. We demonstrate, however, skill complementarity enhances heterophily in the formation of collaboration networks, where people prefer to forge social ties with people who have professions different from their own. We construct a model to quantify the heterophily by assuming that individuals choose collaborators to maximize utility. Using a huge database of online societies, we find evidence of heterophily in collaboration networks. The results of model calibration confirm the presence of heterophily. Both empirical analysis and model calibration show that the heterophilous feature is persistent along the evolution of online societies. Furthermore, the degree of skill complementarity is positively correlated with their production output. Our work sheds new light on the scientific research utility of virtual worlds for studying human behaviors in complex socioeconomic systems. Complexity emerges in the evolving and self-organizing processes of many natural, social, technological, and biological systems. The constituents of a complex system interact with each other and form complex evolving networks, where the constituents are nodes and their interaction relationships are links123457In the sociological literature the local principle of similarity, i.e., the phenomenon that “birds of a feather flock together,” is known as homophily11121310111214151617In general, it has long been accepted that one of the most significant factors in increasing productivity in modern human societies has been the division of labor2425262728293031In this work, we study the collaboration formation process of individuals with different professional skills. A mathematical model is proposed by assuming that individuals in socioeconomic systems choose collaborators that are of maximum utility. Based on the evolving collaboration networks of 124 virtual worlds in which the agents  belong to three different professions possessing different skills, empirical analysis and model calibration unveil that the agents prefer to collaborate with others of different professions. We further construct two measures to quantify the degree of complementarity of virtual societies. We find that social complementarity positively correlates with economic output.s on day t, whose size Ns is the number of s-agents. The number of -agents is denoted by Ns,i, where i = 1, 2, and 3 stand for the three professions. Hence i-agents in society s isConsider a society or a community j-collaborators of an -agent is fs,ij. Hence, the average number of collaborators that an -agent has is j-collaborators in all collaborators of an i-agent isThe average number of qs,ii is the homophily index15i-agents have zero preference for collaborating with j-agents, we have qs,ij = ws,j. If i-agents prefer to collaborate with j-agents, we have qs,ij > ws,j. In this case the i-agents are homophilous when j = i and the i-agents are heterophilous when j ≠ i.Note that s, j)-collaborators that an -agent has is identical to the proportion of j-agents in the group, that is qs,ij = ws,j. Hence the number of -collaborators of an -agent is s, i)-agent, there is an optimal configuration of collaborators with different skills, γij are independent of society s. If the skill configuration in the collaborator list of an agent is optimal, her utility reaches its maximum. If the skill configuration deviates from that optimal value, her utility is reduced. In other words, the utility of an -agent increases when her/his real number fs,ij of -collaborators approaches the optimal value β < 1. Therefore, the utility function of an -agent isAn agent seeks collaborators when she/he finds it difficult to complete a task alone. If there is no collaboration preference, the proportion of -agents for -agents and α > 0 since the second term in i-agents do not have any preference on j-agents such that qs,ij = ws,j for all societies, we have γij = 1. If i-agents prefer j-agents, we have γij > 1. If i-agents prefer not to collaborate with j-agents, we have γij < 1. For {i, j, k} = {1, 2, 3}, if γij > γik, then i-agents prefer j-agents over k-agents. To maintain a collaboration network of size fs,i, the -agent suffers a cost proportional to fs,i in which According to the above model, the overall utility in the decision-making process isDs,i, we can estimate the parameters γij .By maximizing t = 15 of a group of 27 agents randomly chosen from a virtual society filtered by three intimacy thresholds Ic = 0, 100, and 2000. There are 12 warriors, 5 priests, and 10 mages. If i-agents are homophilous  in their collaboration-forging process, the proportion of links between i-agents is greater than  the square of the proportion of i-agents . For Ic = 0, there are 77 links including 15 intra-warrior links, 4 intra-priest links, and 4 intra-mage links. The proportions of intra-profession links are 0.1948 for warriors, 0.0519 for priests, and 0.0519 for mages. For Ic = 100, there are 48 links including 8 intra-warrior links, 1 intra-priest link, and 1 intra-mage link. The proportions of intra-profession links are 0.1667 for warriors, 0.0208 for priests, and 0.0208 for mages. For Ic = 2000, there are 15 links including only one intra-warrior link and no intra-priest and intra-mage links. The proportions of intra-profession links are 0.0667 for warriors and 0 for priests and mages. Hence, the agents in Ic = 0. We will show below that heterophily is not a specific characteristic for these 27 agents but a universal feature presents in all the virtual societies.t = 15 and Ic = 100 most virtual societies have qs,ij > ws,j when i ≠ j, but qs,ij < ws,j when i = j. Such heterophilous patterns are observed for other values of t and Ic as well . We obtain the values of γij for each intimacy threshold Ic on each day t. γij for socioeconomic networks using the intimacy threshold Ic = 100, and Ic = 0, 1, 10, 500, 1000, and 2000. The F-tests presented in Materials and Methods show that all the results are significant at the 0.1% level (see SI Tables).To calibrate the model, we follow and further develop the econometric method presented in ref. γii coefficients are less than 1, while all the γij values for i ≠ j are greater than 1. This indicates that the agents are not seeking same-profession agents but different-profession agents and are thus heterophilous. In most cases, especially when the intimacy threshold Ic is not large, the γij values do not have a trend along the evolution of virtual worlds. When Ic is large, however, we observe an increasing trend in γ13 for Ic = 1000 and 2000, in γ23 for Ic = 1000 and 2000, and in γ32 for Ic = 500, 1000 and 2000 . For each member agent a in t − 6 to t, denoted as Ys,a(t). The economic performance of the agents in To measure the economic implications of heterophilous preference in socioeconomic networks, we investigate the relationship between complementarity of professions and economic performance. Consider the socioeconomic network One measure of profession complementarity can be defined as the sum of preference measures between the three types of agents,qs,ij deviates from the optimal collaborator configuration γijws,j . The lower the deviation, the higher the degree of complementarity. Thus, we haveAlternatively, we can measure complementarity by determining how much the real collaborator configuration Pk−12/Pk2), lg(Ck−12/Ck2) and lg(Yk−12/Yk2), rather than focusing on each society separately. Both measures of complementarity correlate strongly with the relative economic output when t and I are not large (t), most agents strive to achieve higher levels by implementing specific tasks with small economic outputs. Other agents attempt to obtain high intimacy levels by killing monsters in locations unrelated to economic outputs. In both cases the agents intend to form complementary collaboration networks, but their activities are not focused on economic outputs. With the development of a virtual world, the number of active agents increases and reaches a maximum at time tmax and then decays . And so on so forth. These tasks are usually not easy for the associated agents. However, they can ask their collaborators for help to form a team and fulfill the tasks together. Agents can also form teams to kill monsters and make productions. All these collaborations will increase the intimacy of the collaborating agents in the same team.s-agent is an agent belonging to society s. An i-agent is an agent having profession i. Similarly, an i-collaborator is a collaborator having profession i. An -agent or -collaborator is an i-agent or i-collaborator in society s.In each society there are three professions . We use subscripts 1, 2, and 3 to stand respectively for the three professions: warrior, priest and mage. For simplicity, we define several notations as follows. An s, i)-agent solves the following decision-making problem of how many collaborators to haveAn  denotes the average behavior (decision) of all agents having the same profession in a given society. If we consider an arbitrary agent  denotes a has is the sum of a universal (or systemic) term and an idiosyncratic error term. The error term is assumed to have mean 0 and variance σ2. Note that this assumption states that the variance of any agent of any profession is the same.which means that the “realized” number of collaborators agent Ns as the size of society s and ws,i as the fraction of i-agents in society s. Hence the number of i-agents in society s is Nsws,i, and the expectation of the aggregated number of collaborators that i-agents have in society s is Nsws,ifs,i. According to We denote Es,i has mean 0 and variance 2 = 2σ2.where i ≠ j,It follows that, for s:Following ref. s,i,j is 0 and the variance is ϕs,ijσ2, whereAccording to σ2 for any society s. The sum of squared errors Thus the normalized variable Ns as expected. However, ws,i, which is consistent with the setup of our model but different from the model in ref. which is independent of as, bs and cs could be society-specific and are not included in the final objective function of model calibration.One can see that Ic and t, a society is excluded in model calibration if the number of agents having at least one collaborator is less than 500 to ensure that ϵa has enough realizations. Changing this threshold around 500 results in same results. In addition, if the number of societies included in a model is less than 50, we do not calibrate the model because the model has 10 parameters.For each pair of Q2, the taboo search algorithm is adoptedγij ≤ 2 for 9 with the constraint that 0 ≤ γij ≤ 1 or 1 ≤ γij ≤ 2. The parameters in certain cell corresponding to the minimum of Q2 in all cells are obtained as the solution. The normality assumption of fitting errors has been verified by QQ-plots  for each i are not well separated around γij = 1  and a limited amount of the virtual currency How to cite this article: Xie, W.-J. et al. Skill complementarity enhances heterophily in collaboration networks. Sci. Rep. 6, 18727; doi: 10.1038/srep18727 (2016).


Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts. Hierarchical materials and structures are a class of systems which are composed of structural elements which themselves have structure1An equally interesting class of materials and structures are those designed to exhibit auxetic behaviour, i.e. exhibit a negative Poisson's ratio, which means they get wider rather than thinner when uniaxially stretched9101112Despite the advantages of auxetic and hierarchical materials, the concept of an auxetic hierarchical system has been poorly studied171820222325In this study, we propose and discuss a number of hierarchical auxetics based on rotating rigid units , were assigned stiffnesses of ϕ1) were given stiffnesses of ϕ1, which is related to θ1, the angle between through ϕ = θ1 + θ0. Three different cases were considered here, namely: Case I, where the ϕ1-hinges were set to be much stiffer than the θ0-hinges; Case II, where the stiffnesses were set to the exact opposite of those in Case I, and finally Case III, where all the θ0- and ϕ1-hinges were given low stiffness constants, i.e. both hinges were soft.To illustrate some of the properties and versatility of the proposed hierarchical structures, simulations were performed on the simple two-level system illustrated in νyz and νzy obtained from these systems are shown in θ0- and ϕ1- hinges. The change in angles that occur upon the application of on-axis uniaxial stress help us understand the deformations taking place upon loading . It was observed that the level 1 deformations associated with the ϕ1-hinges were much more significant than those of the θ0-hinges at level 0 , as planar ball and spring systems described by a harmonic potential as discussed in Grima y and z-directions.In all three cases, the squares were kept as rigid as possible by using the highest values for the stiffness constants to define the internal 90° intra-square angles and side lengths. Full details of the simulations are provided within the The concept of hierarchical rotating systems was developed by J.N.G. The simulations were performed by L.M., J.I.A. and K.M.A. J.N.G., R.G. and D.A. wrote the main manuscript text while the figures were prepared by L.M. and K.M.A. A.C. and J.B. contributed to the discussion of the manuscript mainly on the medical aspects of the work involved. The work was supervised by J.N.G. and R.G. All authors reviewed the manuscript before submission.ANIM01.gifSupplementary Information


In the cloud, uploading encrypted data is the most effective way to ensure that the data are not leaked. However, data access control is still an open problem in cloud storage systems. To provide an authorization mechanism to limit the comparison of a user’s ciphertexts with those of another, public key encryption supporting the equality test with four flexible authorizations (PKEET-FA) is presented. Subsequently, more functional identity-based encryption supporting the equality test (IBEET-FA) further combines identity-based encryption with flexible authorization. The bilinear pairing has always been intended to be replaced due to the high computational cost. Hence, in this paper, we use general trapdoor discrete log groups to construct a new and secure IBEET-FA scheme, which is more efficient. The computational cost for the encryption algorithm in our scheme was reduced to 43% of that of the scheme of Li et al. In Type 2 and 3 authorization algorithms, the computational cost of both was reduced to 40% of that of the scheme of Li et al. Furthermore, we give proof that our scheme is secure against one-wayness under the chosen identity and chosen ciphertext attacks (OW-ID-CCA), and indistinguishable against chosen identity and chosen ciphertext attacks (IND-ID-CCA). With the application of the Internet increasingly spreading, people have more extensive storage and computing requirements for cloud servers. Users make full use of cloud servers, allowing cloud servers to help them in storing and processing data, reducing the user’s storage burden and computing overhead. Users in different regions can upload data onto and download data from a server, which provides convenience for users to share data. However, servers are also vulnerable to some attacks. If users store their data unencrypted in the cloud server, attackers or malicious internal administrators may access the data stored by users. The solution is for every user to upload encrypted data onto the cloud server. Previous classical encryption schemes cannot realize direct searches or calculations in the ciphertext.In a searchable encryption scheme , the cipA novel PKEET scheme  was firsBilinear pairing is computationally expensive, and to reduce the computational cost, we have attempted to replace pairing with discrete logarithms. We reconstructed an existing concept with a different tool, namely, reconstructing the IBEET-FA scheme with discrete logarithms. This can achieve more efficient searches in ciphertexts encrypted by different public keys, and maintain the nature of flexible authorization in which different authorizations correspond to different permissions. A public key infrastructure is not required.We first defined the scheme and its correctness. Subsequently, a specific scheme IBEET-FA without paring was constructed, and the scheme was proven to be correct. Our scheme is communicationally efficient, and it has a small public key and ciphertext. The scheme is computationally efficient, as the Aut-1, Aut-2, and Aut-3 authorization algorithms and testing algorithms in it all have a small computational overhead.We then define two security models for the scheme, and two types of adversaries, Adv-I and Adv-II. Our IBEET-FA without a pairing scheme achieved OW-ID-CCA security for Aut-A new concept of public key encryption with keyword search (PEKS) was proposed by Boneh et al.  in 2004 A new scheme of PKE with a delegated equality test (PKE-DET) was proposed by Ma et al. in ; in a muA new authorization mechanism for efficient PKEET-FA was proposed by Ma et al. , which cDuong et al.  proposedWe organize the remainder of the paper as follows. The definitions of Trapdoor Discrete Log Groups and Decision Diffie–Hellman Problem are given in Definition 1.A TDL group generator consists of algorithms TDLGen and SolveDL:Definition 2.Let q be the prime order of group G, generator g is gotten from the running result of algorithm Definition 3.Let q be the prime order of group G, generator g is gotten from the running result of algorithm In i and j. The trusted third party generates system parameters for users and cloud service. User i and user j encrypt their data with their public key, and store ciphertext in the cloud server, and the cloud server is authorized to do equality tests on stored ciphertext, but the server does not have the ability to decrypt them. We present the IBEET-FA system model in In our defined IBEET-FA scheme, we give four entities: a cloud server, a trusted third party, and two users labeled as Definition 4.Our IBEET-FA scheme consists of four algorithms: ⊥.i has the public-secret key pair j has the public-secret key pair User i and i’s secret key i’ciphertext i’trapdoor j’ciphertext j’trapdoor Aut-1:i’private key i’ciphertext i’trapdoor j’ciphertext j’trapdoor Aut-2:i’private key i’ciphertext j’ciphertext i’ciphertext i’trapdoor j’ciphertext j’trapdoor Aut-3:i’private key j and j’s secret key i’ciphertext i’trapdoor j’ciphertext j’trapdoor Aut-4:Definition 5.(Correctness): If for any M in the plaintext space, For any possible plaintext i and any possible ciphertext j, if DecryptFor any possible ciphertext Aut-1: For two trapdoors of Aut-2: For two trapdoors of Aut-3: For two trapdoors of Aut-4: For two trapdoors of i and any possible ciphertext j, if Decryptk:For any possible ciphertext Aut-1: For two trapdoors of Aut-2: For two trapdoors of Aut-3: For two trapdoors of Aut-4: For two trapdoors of Adv-I: For Aut-Adv-II: For Aut-According to the nature of our scheme, we use the IBEET-FA security models defined in . Since AUnder chosen ciphertext and chosen identity attacks, We now define the one-wayness security (OW-ID-CCA) against Adv-I for Aut-t  to Decryption queries: Authorization queries: For three types of authorization Aut-(a)i as input, (b)(c)t which has not been queried in extract queries, and sends it to t can not be queried in this phase and We give the advantage definition of Definition 6.If the advantage t  authorization.Proof of Theorem 2.i, where Game1:  1.Hash queries: Suppose (a)i, the oracle picks (b)(c)(d)2.i, challenger Key retrieve queries: For an identity 3.i, ciphertext Decryption queries: For an identity 4.Authorization queries: For Aut-(a)i as the input, (b)(c)t, and t has not been queried in previous extract query, t can not be allowed to query; and in the decryption queries, Game2: It is almost equivalent to Game 1, the modified parts are as follows:R. We can see that E. If Game3: Game2, the modified parts are as follows:It is almost equivalent to R is a random string, we can konw that We design several related games to prove OW-ID-CCA security against Adv-I From all the formulas obtained above, we derive the following formulaTheorem 3.Based on DDH assumption, in the random oracle model our presented IBEET-FA scheme is IND-ID-CCA secure against Adv-II for Aut-γ  authorization.Proof (Proof of Theorem 3). If such an adversary For n key pairs 1.Hash queries:(a)(b)(c)(d)2.i, Key retrieve queries: Given an identity 3.i and a query ciphertext R, making equation M to Decryption queries: For identity 4.Authorization queries: For Aut-(a)i as the input, challenger (b)(c)t, there is a contraint that t can not be queried in extract queriy phase or Aut-1 authorization query phase. 1.i could not be allowed to query;In the key retrieve query phase or Aut-1 authorizations query phase, 2.In the decryption query phase or the authorization query phase, □G, In ize than ,23,24 inize than  in the cIn From the comparison results in In this paper, we propose a new IBE scheme without pairing, which supports the ciphertext equality test. Our scheme introduces the authorization mechanism proposed in the scheme , four tyOur proposed approach can be applied to equality tests over ciphertexts encrypted with different public keys, which increases the application range of cloud computing. Furthermore, our scheme is in IBE settings, avoiding complex key management issues. However, there are security channel key distribution and private key escrow issues in IBE. In the future, we will try to combine the advantages of IBE and PKE to propose more secure and efficient equality test schemes.


The investigation of the link between reduced forced vital capacity (FVC) and risk factors and health variables in women aged ≥ 40 years is encouraged since a reduced FVC was related to all-cause mortality. The high frequency of women with a reduced FVC, observed in some studies, could be related to the impacts of parity on lung. In the literature, the association between parity and health consequences is discussed in terms of “selection pressure”, and the trade-off between longevity and fertility described by scientists is termed the “longevity determination” or “biological warranty period”. The respiratory system could be influenced by parity. Above all, it is the respiratory system, who endures the repercussions of the numerous physio-pathological experiences of the woman life. The probable effects of parity on lung function data, including FVC, make parity a key predictor to be stressed and evaluated. Parity is a promising original direction for physiological and pathophysiological research, particularly for low- and lower-middle- income countries. Thus, upcoming epidemiological and clinical studies of lung function data in women would need to include information about their parity status. Dear editor,ie; the number of offspring a woman has borne) on lung  or a mixed population of healthy/unhealthy women also reported opposing outcomes  initial mean FEV1, ii) rate of FEV1 decline; and iii) COPD incidence between the different groups of parity [1 or FEV1/FVC in never-smokers or in those with low smoking exposure [eg; multiparous women have a tendency to an obstructive impairment; lower flows; lower post-bronchodilator FEV1, and increased Pi levels) [The four studies –15 examies Table . On the f parity , or that levels) –15.Tableeg, telomere length), oxidative stress, coronary heart conditions, stroke, heart-failure, arterial-hypertension, type 2 mellitus-diabetes, renal cancer, and bad health related quality-of-life [To conclude, parity is a promising original direction for physiological and pathophysiological research, particularly for low- and lower-middle- income countries . In the -of-life , 19. In


Nature Communications 10.1038/s41467-022-32795-y, published online 29 August 2022Correction to: The original version of this Article contained an error in Table 1. The correct version of the 11th row of the 2nd column states ‘0.635’ instead of the original, incorrect ‘−0.635’. The correct version of the 12th row of the 2nd column states ‘0.881’ instead of the original, incorrect ‘−0.881’. This has been corrected in both the PDF and HTML versions of the Article.


Solving structural ensembles of flexible biomolecules is a challenging research area. Here, we propose a method to obtain possible structural ensembles of a biomolecule based on small-angle X-ray scattering (SAXS) and molecular dynamics simulations. Our idea is to clip a time series that matches a SAXS profile from a simulation trajectory. To examine its practicability, we applied our idea to a multi-domain protein ER-60 and successfully extracted time series longer than 1 micro second from trajectories of coarse-grained molecular dynamics simulations. In the extracted time series, the domain conformation was distributed continuously and smoothly in a conformational space. Preferred domain conformations were also observed. Diversity among scattering curves calculated from each ER-60 structure was interpreted to reflect an open-close motion of the protein. Although our approach did not provide a unique solution for the structural ensemble of the biomolecule, each extracted time series can be an element of the real behavior of ER-60. Considering its low computational cost, our approach will play a key role to identify biomolecular dynamics by integrating SAXS, simulations, and other experiments. However, revealing their dynamic processes in solution remains challenging.Many proteins are composed of multiple domains that realize complex and sophisticated functions by rearranging their domains flexibly. For example, each domain works together to introduce DNA supercoiling in DNA topoisomerases and each domain cooperates to refold substrate proteins in some foldases9. The SAXS profiles include structural information in the range of approximately 1–100 nm, which is usually wide enough to study structural range of multi-domain proteins or their complexes. SAXS intensity I(Q) is calculated as a function of scattering vector (Q):Small-angle X-ray scattering (SAXS) is a representative experimental technique to study such behavior of biomolecules9: N is the number of atoms in a system, rij is the distance between the i-th and j-th atoms, and fi (Q) is an atomic form factor of i-th atom, which is regarded as a constant in the measured small-angle range.In Eq. , the θ aSince all molecules in a sample solution contribute an experimental SAXS profile, the profile includes information on their structural ensemble. There could be two different types of structural sets of which ensembles reproduce the same SAXS profile. One is a “homogeneous structural set” in which all molecules have a similar structure. The other is a “heterogeneous structural set”. The latter includes the diverse structures, but their averaged SAXS profile reproduces the experimental one. It is difficult to determine which set should be adopted as the state of the molecule in solution. In other words, we cannot judge whether all molecules have similar or diverse structures only from an experimental SAXS profile.10. In the “maximum parsimony” approach, a structural set composed of a small number of models is selected among possible structural sets matching an experimental SAXS profile. For example, the Akaike information criterion or Bayesian information criterion is calculated for possible structural sets, and a structural set minimizing the criteria is chosen12. Many algorithms, such as ensemble optimization, minimal ensemble search, sparse ensemble selection, and maximum occurrence, have been proposed and utilized17.To address this issue, two main criteria are considered in the context of structural modeling; they are reviewed as “maximum parsimony” and “maximum entropy”22. The other approach is to perform parallel simulations with additional potential to reproduce an experimental SAXS profile27.In the “maximum entropy” approach, a free energy landscape derived from a simulation force field is adopted as the prior distribution. The resultant ensemble should match an experimental SAXS profile and be least inconsistent with the force field. A force field does not always reproduce a real structural ensemble of a molecule. Therefore, correction of a free energy landscape to match an experimental SAXS profiles is often effective. There are two ways to correct a free energy landscape while satisfying entropy maximization. One direct approach is reweighting the free energy landscape to match an experimental SAXS profile after structural sampling by molecular dynamics (MD) simulations or Monte Carlo simulationsAlthough both methods are effective, they are not necessarily sufficient to model any biomolecular systems. The structural set composed of a small number of models implies that the resulting structures discretely distribute in a structural space. In a largely fluctuating system, such as a multi-domain protein with intrinsic disordered regions, it is more reasonable to model a structural set which continuously distributes in a structure space.26. In many CG models, each CG bead reproduces net charge and hydrophilicity of their corresponding atom set, resulting in roughly reasonable inter- and intra-molecular interfaces in the simulations30. However, parameter adjustment using experimental data is often required32. A general-purpose CGMD potential does not necessarily guarantee accurate dissociation constant for the interfaces of a biomolecule. Therefore, it may not always be suitable to perform entropy maximization using a free energy landscape from a given CGMD potential as the prior distribution.Maximum entropy approaches are useful in that they can construct a physically reasonable structural set. It is necessary to sufficiently explore possible molecular structures in these approaches. However, sufficient stuructural sampling is often difficult for atomistic MD simulations. Coarse-grained (CG) MD simulation is a useful alternative to overcome this difficultyHere, we propose another approach to enumerate possible behaviors of a biomolecule using an experimental SAXS profile and CGMD simulations. In this method, CGMD simulations are first performed to obtain trajectories that efficiently cover their conformational space. Then, time series that match the SAXS profile are extracted from the trajectories. If the resulting time series are long enough, they reflect information on possible preferred states of the biomolecule; the molecule stays in the stable states for a longer time than unstable ones.3. ER-60 is composed a, b, b′, a′ domains and possesses reaction Cys-Gly-His-Cys (CGHC) motifs in both the a and a′ domains  at each Q value. Therefore, diversity in scattering curves among structures was explained by open-close motion of ER-60. In addition, this linear relationship was indicated as two isosbestic points in Q-I(Q) plot. The actual structural ensemble of ER-60 in solution can be a mixture of these possible domain dynamics. Our method provides "elements of biomolecular motion”, which should be useful in the context of an integrated structural biology including SAXS, MD simulations, and other experiments.We tested our method on a multi-domain protein ER-60, which is a member of protein disulfide isomerase familyins Fig. . The a aWhen stable inter- or intra- protein interfaces appear in CGMD simulations, they are regarded as candidates of actual interfaces, andSince atomistic-scale interactions, such as hydrogen bonds and hydrophobic interactions, cannot be expressed precisely in CGMD simulations, the accurate affinity of the interfaces is not guaranteed.Based on these assumptions, we devised a method to collect a series of structural models that include possible stable states. This is composed of two steps. In step 1, CGMD simulations changing a possible parameter are performed. In step 2, from each of the trajectories, the longest continuous time series that reproduces the SAXS profile is extracted. In summary, we clip a part of a CGMD trajectory that matches a SAXS profile and approximates the actual behavior of the biomolecule as a repetition of the clipped time series. We designate this method “SAS-CLIP”. Although only a single region is clipped from each trajectory, we can expect that possible structural ensembles can be enumerated by applying the SAS-CLIP to multiple trajectories. This point is studied in the “To compose a series of structural models that reproduces a SAXS profile, we made the following two assumptions about CGMD:35. Before CGMD simulations, it was necessary to clarify the structural stability of three folded regions, from Ser25 to Pro134 (system a), that from Ala132 to Lys366 (system b-b′), and from Tyr364 to Glu493 (system a′). For this purpose, single atomistic simulations for the three systems were first performed.All simulations were performed using GROMACS 2020.420. The Lennard–Jones potential between i-th and j-th particles is described as:CGMD simulations were performed using the Martini 3 open-beta version. In the CGMD simulations, the Lennard–Jones potential between water and ER-60 was scaled, as in previous reportsij as a parameter. When i-th and j-th bead pair is water-protein bead pair, the εij is treated as λWP εij,default. Here, the εij,default is the default value in the Martini 3 open-beta version, and λWP is the scaling factor for water-protein interactions. The σijs are constants depending on bead type, and rij is distance between i-th and j-th particles. First, we performed three 5000-ns production runs with λWP values of 1.0, 1.01, 1.02, 1.03, 1.04, 1.05, and 1.06. According to the results  and Isim,j (qi) are the scattering intensities of experimental SAXS profile and calculated scattering intensity of j th model, respectively. The theoretical profiles are normalized by Isim,j(0). c and offs are adjustment parameters. The latter parameter explains possible mismatch between buffer solution and sample solution in the experimental SAXS profile. The parameters are determined by the condition: The χThe distance distribution function p (r) was calculated using the reverse-mapped atomistic model. For the calculation, all electrons were considered to be in the center of an atom, and hydrogen atoms were ignored.t was calculated by multiplying the number of snapshots in the time series by 2 ns/frame.Since snapshots were acquired every 2 ns for analysis, the duration time of the time series L38, where ER-60 consists of three domains: from Ser26 to Lys130 (a domain), from Phe160 to Asp355 (b-b′ domains), and from Pro377 to Arg482 (a′ domain). In previous reports, ER-60 was treated as four domain protein4, where the b-b′ domain was further divided into b and b′ domains. The θa-b-b′, θb-b′-a′, and φa-b-b′-a′ are angles formed by centers of mass (COMs) of the three domains or dihedral angle formed by COMs of the four domains  and φb-b′-a′-CGHC(a′) are angles formed by COMs of the three domains and the COM of the CGHC motif of either the a or a′ domain. The Da-a′ is distance between COMs of a and a′ domains. The COM of each domain or CGHC motif is defined as the averaged coordinates of backbone beads of the corresponding residues  probability map between a clipped time series with the SAS-CLIP and its original trajectory  was evaluated using the following Kullback–Leibler divergence:The difference in the shape of the  is the probability at  of a clipped time series, and Poriginal  is the probability of the original trajectory. KLSAS-CLIP only considers the region where PSAS-CLIP  > 0 and their vicinity. In other words, the sum was calculated only for C1 and C2 are defined as follows  | PSAS-CLIP  > 0}C2. { | Adjacent to C1}These conditions allow KLSAS-CLIP to be small when ER-60 stays only in a few (or one) of several stable states. Considering that the KLSAS-CLIP ignores outside the original  is normalized to meet the following relationship:39.Graphs and figures were created using gnuplot and inkscape. Images of protein structures were created using PyMOL4 because the SAXS profile calculated from crystal structure did not reproduce the experimental structure. To clarify the origin of this discrepancy, we first examined the dynamics of each folded structure. We performed atomistic MD simulations of three parts of ER-60, including the a, b-b′, and a′ domains. In any of the three simulations, root mean square deviation (RMSD) of the folded region between a simulation snapshot and the crystal structure distributed at approximately 1.5 Å  of #A-1, #A-2, and #A-3 were 2690, 2208, and 1462 ns, respectively  probability distribution between a clipped time series and its original trajectory  of this Q contains information on domain conformation. That is, the SAS-CLIP could extract structural series with incorrect domain conformation even with small χ2. According to the observations, we improved the criteria: satisfying both “χ2 < 3.0” and “the −1”.Second, the criterion for reproducing the experimental SAXS profile, which was initially χÅ−1 Fig. a. This Qt. We focused on the relationship between λWP and Lt. When λWP was small, Lt of the clipped time series tended to be small . In the second group, θa-b-b′ was distributed at < 90° . While the structural trends were common, the detailed distributions differed from each other. Additionally, we examined the dihedral angle φa-b-b′-a′. φa-b-b′-a′ distributed between − 15° and 75°  and φb-b′-a′-CGHC(a′) for the six time series. In terms of the domain orientations, one or two preferred ones were observed for each time series. The preferred orientations also differed between the time series. In other words, the SAS-CLIP enumerated the possible distributions of the orientations of the a- and a′-domains.Subsequently, we examined whether the a-b-b′ and θb-b′-a′ with high appearance probability are shown in Fig. 483-Leu505) bridged a and a′ domain. These were temporary bridging in the #B-2. Similar bridging was observed in #B-1, #B-3, #B-4, and #B-5, with lifetimes varying in the range 40–160 ns. The C-terminal loop might contribute to the functional motion of ER-60 via the domain bridging.Finally, the tertiary structures of ER-60 in the clipped ensembles were overviewed. Several structures featuring θa- and a′-domains were more diverse among the clipped ensembles.In summary, we confirmed that SAS-CLIP can enumerate a variety of ensembles of ER-60. The four-domain architecture could be roughly classified into two classes, whereas the detailed conformational distribution differed among the clipped ensembles. The orientations of the 40, an isosbestic point suggests existence of a variable having a approximate linear relationship with the scattering intensity as follows;Reflecting the structural diversity in each clipped ensemble, their calculated scattering profiles were also diverse Fig. . We next0 is a parameter. The difference in I(Q) between molecular structures corresponds to difference in the X. Therefore, the X is a conformational coordinate.Here, X is the variable and X−1 and Q = 0.2 Å−1. In addition, intersections of the curves were concentrated at two regions around Q = 0.12 Å−1  distribution, p(r) showed sharp distribution between 50 and 60 Å  plot. We verified this linear relationship for the ensembles of ER-60 obtained with SAS-CLIP. In Fig. 0 Å Fig. . The two0 Å Fig. . Based oa and a′ domain (Da-a′) approximately linearly correlated with I(Q) , the relationship was common to the six ensembles  Fig. . Here, ta and a′ domains.In summary, our result supports that a single molecular motion can explain diversity of I(Q)s in a structural ensemble when an isosbestic point is found in Q-I(Q) plot. In ER-60, that was open-close motion of the SAS-CLIP does not provide a unique solution of the structural ensemble of a biomolecule. The structural ensemble obtained by this method differ from each other, but they all reproduce the same SAXS profile. This also means that any combination of these time series also reproduce the experimental SAXS profile. Additionally, the structural distribution of each clipped time series approximates that of a long-term MD simulation. Therefore, each time series obtained by SAS-CLIP can be an element of motion of a biomolecule, and any combination of these are candidates for the real structural ensemble.X as a quantity obtained in an experiment other than SAXS, X will be expressed as follows:XSAS-CLIP,i is the quantity for i-th structure series of the SAS-CLIP, which is averaged over all structures in the i-th series. ci is a weight factor. A reasonable structural ensemble that is consistent with any of SAXS, CGMD, and another experiment can be obtained by simply determining the cis. We can assume a variety of data are the quantity X. In fact, many experimental data represent the average quantity over all molecules in solution. In addition, many kinds of experimental data can be calculated from a given atomistic structures. For example, the profile of small-angle neutron scattering (SANS)44, chemical shift for nuclear magnetic resonance (NMR)46, and efficiency of fluorescence resonance energy transfer (FRET)47 can be calculated from tertiary structures. The proposed method has at least two advantages. First, the method is advantageous for constructing realistic ensembles of highly flexible biomolecules; Combination of clipped ensembles with SAS-CLIP results in an ensemble with a very large number of structures. Second, resultant ensembles are consistent with a force field of MD simulation regardless of ci values. The linear combination approach can also avoid the possible effect of artificial free energy minimum derived from an incorrect simulation force field, which is often a problem in the entropy maximization approach. Sufficient ensembles should be clipped to perform such an analysis.Here, we propose a method to identify a structural ensemble of a biomolecule using clipped time series and another experimental data. With SAS-CLIP can be applied to atomistic MD simulations. It is easier for the atomistic simulations to compare a simulation step with real time. When the SAS-CLIP is applied to atomistic simulations, extracted time series will be useful to analyze experimental data including temporal information, such as neutron spin echo.t is large, KLSAS-CLIP is sufficiently small (Table When Lll Table . If we rIn practice, there are three major advantages of SAS-CLIP. First, time series can be extracted from relatively short MD simulations with low computational cost. We can obtain many time series at the same time when multiple simulations are performed in parallel. Second, obtained structural sets reflect a force field of MD simulations, and thus they are candidates of “element of motions”. Third, this method makes it easy to obtain a structural ensemble which matches SAXS, MD, and another experiment with simple linear model. This method will provide a new way to study biomolecules by integrating various type of experiments.Supplementary Information.


Dear Editor,We would like to address the manuscript entitled “Transcanal endoscopic myringoplasty: A case series in a university center” by Garcia et al.The authors write, in the Materials and Methods: “All patients older than 12 years with a diagnosis of non-suppurative, non-cholesteatomatous COM sequela, or with traumatic perforations without spontaneous resolution for more than three months, were included in the study. The diagnosis was based on anamnesis, physical examination, audiometry, and impedance audiometry”.n = 19) of patients three months after intervention.”The authors write, in the Materials and Methods: “The technique and the surgical instruments used were the same as in routine surgeries with microscope, except for the non-use of the microscope andotologic speculum, and the use of the Storz rigid endo-scopes, 4 mm diameter and 18 cm long, at 0° angulation ”.In brief, the transcanal endoscopic approach is excellent for performing cartilage myringoplasty, reducing both the surgical time and complications. However, both the surgical indications, and careful consideration of the outer diameter of the endoscope, are very important, and long-term follow-up is required.The author declares no conflicts of interest.


Since the beginning of the coronavirus disease 2019 pandemic, there has been an explosion of sequencing of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, making it the most widely sequenced virus in the history. Several databases and tools have been created to keep track of genome sequences and variants of the virus; most notably, the GISAID platform hosts millions of complete genome sequences, and it is continuously expanding every day. A challenging task is the development of fast and accurate tools that are able to distinguish between the different SARS-CoV-2 variants and assign them to a clade.k-mers that match SARS-CoV-2 marker variants.In this article, we leverage the frequency chaos game representation (FCGR) and convolutional neural networks (CNNs) to develop an original method that learns how to classify genome sequences that we implement into CouGaR-g, a tool for the clade assignment problem on SARS-CoV-2 sequences. On a testing subset of the GISAID, CouGaR-g achieved an k-mers that capture relevant biological information that distinguishes the clades, known as marker variants.By combining FCGR and CNNs, we develop a method that achieves a better accuracy than Covidex (which is based on random forest) for clade assignment of SARS-CoV-2 genome sequences, also thanks to our training on a much larger dataset, with comparable running times. Our method implemented in CouGaR-g is able to detect https://huggingface.co/spaces/BIASLab/sars-cov-2-classification-fcgr. CouGaR-g is also available at https://github.com/AlgoLab/CouGaR-g under the GPL.The trained models can be tested online providing a FASTA file (with 1 or multiple sequences) at  All these data are stored in publicly available archives, such as the European Nucleotide Archive (ENA) and GISAID  is a square matrix where each entry i, jc is the number of elements that belong to the true class i and were classified in the class j, and the sum of the entries in C is exactly S.Given a classification problem on accuracy of the model is defined as the proportion of the corrected classified samples over the total number of samples; this value ranges between 0 and 1, where 0 means that all samples were erroneously classified, while a value of 1 means a perfect classification. It can be defined in terms of the entries of the confusion matrix as follows:The Matthews correlation coefficient (MCC), proposed in , where 1 is perfect classification, −1 is the opposite, and 0 means that the confusion matrix is all zeros but for one single column, or when all entries are equal, The posed in  as a binposed in , and it posed in  for detaocument} .In order to assess the quality of the class separability given by the CNN, we evaluate the embeddings of the last layer (the one used to perform the classification) in the network with 3 clustering evaluation measures. These embeddings are the output from the final layer of the network for each FCGR.Silhouette coefficient [v belonging to a cluster A, the silhouette coefficient s(v) of v compares the mean intracluster distance in A (a) with the mean nearest-cluster distance for v (b), that is, the closest cluster to v different from A.fficient . Given as(v) ranges between −1 (wrongly assigned) and 1 (perfect separability). For a cluster A, the mean silhouette coefficient of A is computed as the average of s(v) over all embeddings v ∈ A.The value of Calinski–Harabasz score [E of size En that has been clustered into k clusters, the Calinski–Harabasz score s, also known as the variance ratio criterion, is defined as the ratio of the between-clusters dispersion and the intercluster dispersion for all clusters (the dispersion of a group of n points is measured by the sum of the squared distances of the points from their centroid).tr(kB) is the trace of the between-cluster dispersion matrix and tr(kW) is the trace  of the within-cluster dispersion matrix, defined as follows:qC is the set of embeddings in the cluster qq, c is the centroid of the cluster q, and Ec is the centroid of E and qn = |qC|.sz score . Given as means that the clusters are dense and well separated.The higher the score GDV [GDV N D-dimensional embeddings {x1, …, Nx}, with nx =  and a set of L classes {C1, …, LC}, where each nx is assigned to one of the L distinct classes. Consider their z-scored points , with is = , where d. Using the rescaled data points ns = , the GDV Δ is calculated from the mean intraclass and interclass distances as follows:Given a set of lC is defined aslC and mC is defined as follows:kN correspond to the number of points in class k, and ith point of class k. The quantity d is the distance between a and b; for our case, we considered the Euclidean distance. The value Δ range is between −1 (perfect separability) and 0 (wrongly assigned).where the mean intraclass for each class k-mers for the classification of each clade.After the model is trained, we can perform feature importance methods  to analyze the impact of each element of the FCGR in our prediction. We selected saliency maps  and SHAPk-mers for the classification of each clade in the trained models.Using these methods, we aim to analyze the most relevant Project name: Classification of SARS-CoV-2 genome sequence with CGR and CNNRRID:SCR_022952)Project home page: CouGaR-g (Operating system(s): e.g., Platform independentProgramming language: Python 3.10.5Other requirements: Python 3.10+, tensorflow 2.10.0, scikit-learn 1.1.2, tqdm 4.63.0, pandas 1.5.0, biopython 1.79, Pillow 9.0.1, matplotlib 3.5.1, shap 0.41.0, opencv-python 4.6.0.66License: GNU GPLThe list of FASTA sequences and metadata can be downloaded from  after crA web app version of CouGaR-g with all the trained models is available online at .GigaScience GigaDB database [All supporting data and materials are available in the database .CGR: chaos game representation; CNN: convolutional neural network; ENA: European Nucleotide Archive; FCGR: frequency matrix of chaos game representation; GDV: generalized discrimination value; SVM: support vector machine.The authors declare that they have no competing interests.This project has received funding from the European Union’s Horizon 2020 Innovative Training Networks program under the Marie Skłodowska-Curie grant agreement No. 956229.This project has received funding from the European Union’s Horizon 2020 Research and Innovation Staff Exchange program under the Marie Skłodowska-Curie grant agreement No. 872539.J.A.C. and S.A. wrote the code, prepared the data, and performed the experiments. J.A.C., S.A., S.C., P.B., and G.D.V. devised the methods and analyzed the results. J.A.C., S.C., and G.D.V. designed the experiments. All authors contributed to finalizing of the manuscript.giac119_GIGA-D-22-00106_Original_SubmissionClick here for additional data file.giac119_GIGA-D-22-00106_Revision_1Click here for additional data file.giac119_GIGA-D-22-00106_Revision_2Click here for additional data file.giac119_Response_to_Reviewer_Comments_Original_SubmissionClick here for additional data file.giac119_Response_to_Reviewer_Comments_Revision_1Click here for additional data file.giac119_Reviewer_1_Report_Original_SubmissionDominik Heider -- 6/1/2022 ReviewedClick here for additional data file.giac119_Reviewer_1_Report_Revision_1Dominik Heider -- 10/26/2022 ReviewedClick here for additional data file.giac119_Reviewer_2_Report_Original_SubmissionRiccardo Rizzo -- 7/19/2022 ReviewedClick here for additional data file.giac119_Reviewer_2_Report_Revision_1Riccardo Rizzo -- 10/25/2022 ReviewedClick here for additional data file.