The operation of a human-machine interface is increasingly often referred to as a two-learners problem, where both the human and the interface independently adapt their behavior based on shared information to improve joint performance over a specific task. Drawing inspiration from the field of body-machine interfaces, we take a different perspective and propose a framework for studying co-adaptation in scenarios where the evolution of the interface is dependent on the users' behavior and that do not require task goals to be explicitly defined. Our mathematical description of co-adaptation is built upon the assumption that the interface and the user agents co-adapt toward maximizing the interaction efficiency rather than optimizing task performance. This work describes a mathematical framework for body-machine interfaces where a naïve user interacts with an adaptive interface. The interface, modeled as a linear map from a space with high dimension (the user input) to a lower dimensional feedback, acts as an adaptive “tool” whose goal is to minimize transmission loss following an unsupervised learning procedure and has no knowledge of the task being performed by the user. The user is modeled as a non-stationary multivariate Gaussian generative process that produces a sequence of actions that is either statistically independent or correlated. Dependent data is used to model the output of an action selection module concerned with achieving some unknown goal dictated by the task. The framework assumes that in parallel to this explicit objective, the user is implicitly learning a suitable but not necessarily optimal way to interact with the interface. Implicit learning is modeled as use-dependent learning modulated by a reward-based mechanism acting on the generative distribution. Through simulation, the work quantifies how the system evolves as a function of the learning time scales when a user learns to operate a static vs. an adaptive interface. We show that this novel framework can be directly exploited to readily simulate a variety of interaction scenarios, to facilitate the exploration of the parameters that lead to optimal learning dynamics of the joint system, and to provide an empirical proof for the superiority of human-machine co-adaptation over user adaptation. Interfaces between human and a machine are at the forefront of research in human augmentation  within which the generative model Let us now consider a set of samples {diag, where λn are the eigenvalues of V = [v1|…| vn] with the corresponding eigenvectors as columns such that:We can find a more interesting expression for Equation (7) considering the set of input vectors centered in the mean: Using Equation (8), we can then rewrite Equation (7) in the case of random variables with zero mean:C = BV. We can immediately see from Equation (9) that the expected reward will be maximized if CCT = I, hence if V = B†. This is equivalent to say that the reward will be maximized if the user learns to generate inputs that lie in the potent space of the interface map.where We have assumed the user could be modeled as a non-stationary generative process characterized by a certain expected value and covariance matrix at a certain instant of time. In the following paragraph we will now provide a mathematical formulation for iteratively computing the parameters of the user distribution based on the feedback received by the interface and the reward.qk is received, the sample estimates for the mean and the principal components of the covariance matrix can be updated as follows:Given that the user receives feedback as a continuous stream, the distribution parameters should be estimated following an incremental approach. In the following, we will report the formulation originally proposed by Weng and colleagues , where T is the sampling interval and η the learning rate. Hence, the η parameter describes how fast new data is incorporated in the model or, equivalently, how quickly the user is willing to discount older memories. It has been suggested that the learning rate should be chosen within the range  to ensure convergence and stability of the solution  and (11) effectively implement a first order exponential smoothing filter with time constant τ = −k = η the model would effectively mimic a process that is referred to as “use-dependent” or “experience-dependent” learning , at each iteration the learning rate will always be bounded between zero, whenever the current action receives zero reward, and η. It is interesting to note that for ηThe last component of the model that has to be addressed is how the process of action selection is carried out. In a real scenario, the user would select actions directed toward a goal, for instance to reach a target position with the computer cursor or when carrying out a pursuit task. As we are not interested in modeling the behavior of the user under specific task conditions, we will only include in the model the general requirement that the samples drawn by the user ought to be statistically dependent.L by filtering successive randomly drawn inputs {qk, …, qk+L} with a first order autoregressive exponentially weighted moving average (ARMA) model, initialized with s0q=0:In practice, we simulate data to be dependent within a certain window The parameters values α = 0.99, β = 0.15 have been chosen to resemble the correlation encountered in experimental data sequences from upper-limb movements after centering the data in the mean  and (11) that the user distribution will progressively shrink until the variance becomes zero.k at each time step:In order to prevent the user from learning degenerate solutions and to avoid the problem of the “vanishing variance,” we need to introduce two regularizing constraints on the structure of the covariance matrix used to generate data at each step. In particular, we assume here that the user is motivated in producing actions that span (at least) two dimensions. This motivation is then translated into a corrective term for the variance matrix ΛλC is a n-dimensional vector of corrective factors and z is a n-dimensional vector of random noise.where The first constraint, formalized in Equation (15), imposes that the vigor of the user's actions in the task dimensions over time has to remain constant. No constraint is imposed on the cumulative variance distributed along the remaining dimensions.m eigenvalues does not decrease compared to the initial condition.The second constraint imposes that the percentage of variance accounted for by the first BV(BV)T = I. If the interface is static, this can be achieved only if the user learns to generate data points that lie in the potent space of the map. However, this process is likely to develop over a prolonged period of time as a result of the interaction of multiple learning mechanisms with task constraints  to iteratively update the orthogonal components of the map to resemble the first eigenvectors of Σb is the first column vector of B. The expression can be easily generalized to multiple orthogonal components but, for brevity, we let the reader refer to Weng et al. . The dimensionality of the input data and the interface have been chosen to match the ones in our previous experimental study, where 10 individuals learned to control a 2D cursor moving their upper limbs  was chosen to be 10−4.We ran multiple simulations with 20 different values of learning rate logarithmically spaced between 10The simulation steps are summarized in We then asked whether the model was able to fit the actual user distribution parameters recorded during the reaching task. We modified In this scenario, both the user and the interface parameters are allowed to change following the steps described in −4 and 10−1. Hence, we trained a total of 400 models over 40,000 iterations 20 times, each using different random seeds.We simulated all the possible combinations for the learning rate of both the user and the interface considering 20 log spaced values between 10The interface map and the virtual user's distribution parameters were once again initialized using participant #S8 as a reference, to allow comparing the results across the different scenarios.We computed three metrics to assess the evolution of the user covariance manifold in relation to the interface map across samples. These metrics are commonly used to assess user learning in body-machine interfaces as well as other redundant control tasks  we expect the user to progressively reduce the probability of generating actions along the dimensions associated with a null feedback. Experimental data confirmed that body-machine interface users learn to increase planarity in a 2D task  subspaces will have a Subspace Angle close to 0 deg, while 90 deg indicated that the two subspaces are orthogonal and share a minimal projection. It is computed as the angle between the hyperplane described by the map and the hyperplane described by the first two principal component of variance extracted from the user distribution at each iteration: VAF: Variance Accounted For by the interface map, varies from 0 to 100% and quantifies the percentage of user covariance that is transferred to the feedback though the interface map. This metrics effectively encodes the average reward associated with the current user distribution and can be considered a measure of control efficiency. It is computed every iteration as: Rate of convergence [samples]: quantifies the number of iterations needed for the user to improve performance by 63% while converging toward a stable solution either independently or jointly with an adaptive interface. It is computed over the values of Subspace Angle between the user and the interface over training as the time constant of the single exponential function that yields the best least square fit to the data.In order to evaluate the proposed metrics over the experimental data, the parameters of the covariance matrix through time were estimated using a sliding window of 3,000 samples (60 s of data) over the recorded data sequence.Here we consider the effect of the choice of the learning rate parameter on the ability of a simulated user to maximize the expected reward over time when interacting with a static map (γ = 0). We will first consider the plausibility of our simplified model of user learning by testing its ability to emulate the performance metrics extracted by the experimental data recorded from 10 actual users of our previous study .The evolution of Planarity and Subspace Angle across iteration for all the 10 participants considered is depicted in After having verified the plausibility of our model, we simulated a virtual user in a body-machine interface scenario using the algorithm outlined in Panels A and D show how the expected reward changes across iterations as a function of the user distribution and the interface map. The results show that assuming data to be dependent does not affect the course of Planarity of the generative model covariance. However, this assumption greatly impacts the distance between the model distribution and the interface map. As suggested by the difference in the values of Subspace Angle obtained in the case of independent , panel BA first important observation is that the assumption that the data is independently distributed affects the relationship between the learning rate parameter and model convergence. From −4 to 10−1.This observation finds its counterpart in the experimental evidence that every user develops a unique solution to the interface control problem, as exemplified by In summary, these results suggests that (i) the particular solution an interface user may converge to depends strictly on the patterns of input covariance generated during learning and that (ii) it is virtually impossible to accurately predict the learning trajectory of an interface user unless the exact sequence of control actions is known.This section summarizes the results obtained simulating a set of user-interface dyads with different combinations of the respective learning rate parameters η and γ. Here we assumed that the user generates a sequence of dependent inputs, and both the user and the interface adapt their parameters every iteration step. The interface's goal is to minimize information loss and the user's implicit objective is to maximize the expected reward over time through action reinforcement. Results obtained during co-adaptation are contrasted with simulation results of user learning with dependent and independent data sequences but without interface adaptation in terms of (i) final performance  and (ii)i = γi: 0.87 ± 2.0 deg), while the least favorable conditions occurred when a fast-adapting interface (γ ≥ 10−2) was combined with a very slow learner (η < 10−3) and whenever a very fast learner was paired with a slow-adapting interface. Notably, co-adaptation yielded considerably smaller Subspace Angle on average (11.5 ± 12.6 deg) compared to a user learning through dependent data sequences for any combination of learning rates ]. This subspace is depicted in the top panels of B represents the subspace of the cursor coordinates defined by the interface map, the gray hyperplane represents the subspace spanned by the first two components of body movement variance (B and k = 1000 from a model of a user learning with η = 0.0013 vs. a model of user-interface co-adaptation with η = γ = 0.0013. The six body trajectories are shown in black starting from the center (gray circle) and ending each in a red circle. The bottom panels show the projection of the body trajectories on B (in blue). As previously noted, user-interface co-adaptation allows maximizing the amount of movement that projects into cursor displacements compared to user learning, yielding to a minimal distortion between the intended and perceived trajectory. The subspace angle between B and Firstly, interface co-adaptation does not eliminate the need for user learning. In fact, Secondly, user-interface co-adaptation yields better performance than user learning alone, as the relative distance tends to zero for suitable choices of interface adaptation rate  = 44.29, p < < 0.001], with greater change induced by faster-learning users (about 10 degrees more than slower users). The effect of the interface change is more marginal  mostly due to the high variability across repetitions, as a post-hoc test with Bonferroni correction only identified one significant comparison at the significance level of 0.01 (γ = 0.0001 vs. γ = 0.0055). No effect of the interaction between user and interface learning rates was found .Lastly, the particular choice of γ seems to have a very marginal influence on the amount of change in the interface map compared to the initial condition  tested in De Santis et al.  co-adaptation leads to greater control efficiency than what the user would have otherwise attained and allows reaching a stable equilibrium faster. We found that, for a given user learning rate, interface efficiency could be maximized for a relatively broad range of interface adaptation rates. However, choosing an adaptation rate similar to the time scale of user learning would lead to the best performance, both in terms of steady state solution and in terms of stability. This result seems to disagree with that of Igual et al. , where is et al. , and thes et al. .One point should be stressed. Interface co-adaptation is a viable way to optimize interface control, but it does not eliminate the need for user learning. Plug-and-play interfaces . This phenomenon may be amplified whenever the learning rate imbalance triggers instability in the interface map. For an appropriate choice of learning rates, this effect is expected to rapidly disappear as soon as the system reaches an equilibrium.Finally, as we have focused our investigation on the impact of co-adaptation on the convergence and stability of the system in the initial phases of learning, we have not specifically addressed the problem of stability over a long period of time. Nevertheless, the results from simulations foster the idea that the joint system reaches a point of equilibrium, suggesting that the solution could be stable over extended interaction despite the adaptive model having a constant learning rate. It is however possible that non-stationary adaptation rates for the interface may lead to further stability enhancement.dalia.desantis@gmail.com.The data analyzed in this study is subject to the following licenses/restrictions: The code and the datasets generated and analyzed for this study are available from the corresponding author on reasonable request. Requests to access these datasets should be directed to Dalia De Santis, DD conceived the work, formulated the model, carried out model simulations, data analysis and interpretation, drafted the manuscript, revised, and approved the submitted version.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be constructed as a potential conflict of interest.


Scientific Reports 10.1038/srep23100, published online 14 March 2016Retraction of: The Editors have retracted this Article.There appears to be partial overlap of the actin panels presented in Figure 2AThere appears to be a high level of similarity between the actin bands presented in Figure 3AThere appears to be duplication within the panels presented in Figure 3CThere appears to be duplication within and between the panels presented in Figure 3DThere appears to be duplication of the panels for β-actin in Figure 4CIn addition, the last author has stated they were not able to locate all the original data files. The Editors therefore no longer have confidence in the reliability of the data reported in the Article.Several of the figures presented in this paper appear to contain duplications that are not compliant with the digital image and standards policy of the journal, specifically:The authors have not responded to correspondence regarding this retraction.


Unconventional dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be avoided in the presence of many-body localization. A discrete time crystal represents a driven system whose local observables spontaneously break time translation symmetry and retain memory of the initial state indefinitely. Here, we report the observation of a discrete time crystal on a chain consisting of 57 superconducting qubits on a state-of-the-art quantum computer. We probe random initial states and compare the cases of vanishing and finite disorder to distinguish many-body localization from prethermal dynamics. We further report results on the dynamical phase transition between the discrete time crystal and a thermal regime, which is observed via critical fluctuations in the system’s subharmonic frequency response and a substantial speedup of spin depolarization. The time crystal phase has been observed, and a first step toward establishing a dynamical phase diagram has been obtained. The phenomenon of spontaneous symmetry breaking is common in nature and characterizes a large class of phases in materials. For instance, the crystal lattice of a solid formed by the nuclei breaks the continuous spatial translation symmetry of the underlying Hamiltonian, as indicated by the mere discrete translation symmetry of the local density operator. In 2012, Wilczek proposed the existence of phases of matter that break continuous time translation symmetry . MBL has been a subject of extensive research in recent years, both theoretical and experimental ; these additional terms make the model nonintegrable and truly many-body (see Discussion).We implement a periodically driven Ising chain with quenched disorder and imperfect drive. This is an instance of Floquet evolution, i.e., time evolution defined in terms of a unitary U. In Z. The error rates on current NISQ devices limits the number of Floquet periods to ∼50. By making use of the heavy hex topology of ibmq_brooklyn and ibmq_manhattan iZ(t)〉. It is convenient to consider the averaged autocorrelator qN is the number of qubits. Rapid decay of these correlators is expected for the thermal regime; in contrast, the oscillations in theory persist indefinitely for the DTC because of MBL. The inherent noise of NISQ devices causes depolarization of the qubits and represents the main challenge for distinguishing between DTC and thermal regime. Even in the ideal case of ϵ = 0, where U should not generate any entanglement for an initial product state, we observe a finite rate of decay. Figure 3A shows the averaged autocorrelator after correcting for measurement errors. For ϵ = 0.05, we observe persistent oscillations as a hallmark of the realized DTC. Deviations from ±1 are attributed to a combination of noise and the fact that the conserved operators of the effective MBL Hamiltonian do not exactly coincide with the set of operators {iZ}; hence, the iZ are only partly conserved at late times. Nonetheless, the oscillators are stable over 50 Floquet periods and are clearly distinct from prethermal dynamics iZ(t)> at half the driving frequency ωD = 2πT−1 for each spin. We show the qubit-averaged Fourier spectrum in D/2 is pronounced; the mitigation scheme almost doubles the peak height.The DTC phase can also be observed through a pronounced peak in the Fourier spectrum of <In In the following, we focus on the dynamical phase transition from the DTC regime to the thermal phase. It can be shown  Hamiltonian is given byThe approximate sign indicates that the representation in terms of a conserved Hamiltonian is not correct out to temporal infinity and that the effective Hamiltonian itself contains higher-order terms that we neglect 〉}(ωD/2)∣, with ℱ{ · } representing the Fourier transform, one can conclude that the variance across the chain Var({ih}) should vanish in the DTC phase and in the thermal phase. At the transition, we instead expect critical fluctuations to produce a finite value. For short chains (N ∼ 10), one has to average over several disorder realizations to obtain a clear signal because the behavior at the transition is sensitive to the particular choice of disorder. Our system of N = 57 sites seems to produce a rather clear signal without this averaging process, as one might expect. c ≈ 0.075 (the peak’s maximum) as an estimate for the phase transition. Finite values at very small values of ϵ may be attributed to the aforementioned fact that only part of iZ is actually conserved at late times.This leads us to the first indicator of the phase transition, namely, critical fluctuations at the transition between the DTC and the thermal phase in the order parameter that spontaneously breaks the Ising symmetry in one phase but not in the other. The order parameter of the random Ising transition is the iZ > ∣ (t) ∝ exp ( − δit), we define c ≈ 0.075.The second indicator of the transition is the average decay constant U3 = exp {(−i∑ibiZi)}, where the random amplitudes ib can be at least as large as π/25. In addition, further spin-spin interactions are generated . We therefore argue that the actual model, as implemented on the quantum computer, is truly interacting and thus qualifies as MBL. This is in line with the reasoning and numerical evidence put forward in ∣ = 1This empirical approach requires the input of at least two data points at different times. To not overcorrect the measurements at early times, where systematic gate errors have not yet accumulated to the same extent as for late times, we choose to normalize the polarizations to ∣< Z>final represents an average over a few data points at the latest simulated times. The average is taken to avoid the effects of changing conditions over the course of the simulation. From this, one can, in principle, extract the effective empirical error parameters<In addition to the measurement and gate errors, one can also observe an overall exponential decay of polarization due to the qubits thermalizing with their environment. To compensate for this decay, we would like to rescale the data accordingly. We use the following algorithm to distinguish between a qubit being nonpolarized at late times due to internal thermalization versus due to erroneous spin flips:W0 ∈ , where 1 corresponds to the maximal polarization of a qubit. Qubits whose average polarization over 5 time steps drops below W0 after the initial 13 time steps for ϵ = 0 are excluded from the evaluation (further justification below).1. Introduce a cutoff parameter Wf < W0 for finite values of ϵ. Qubits that lie within the interval  after the initial time evolution are assumed to approach vanishing magnetization due to thermalization, in which case, the accumulated gate error in the magnetization is less relevant (<σz > = 0 is a fixed point as far as the Trotter gate errors are concerned). Therefore, we do not rescale the subsequent data points for these qubits.2. Introduce a fixed threshold ith qubit at time t as measured on the quantum computer and corrected for measurement errors, the exponential fit of the reference data at ϵ = 0 takes the form3. For qubits outside of this interval, one can assume that most of the damping is due to the same depolarizing noise that was observed previously for ϵ = 0. We rescale the subsequent data points with an exponential fit obtained from the ϵ = 0 data for this qubit but adjusted by the ratio of average polarization for a given finite ϵ to the corresponding average polarization for vanishing ϵ. With W0] even for ϵ = 0, because we would otherwise confuse them for ones that are thermal. This justifies step 1 in the above error mitigation scheme.The bar denotes an average over 5 time steps after the initial 13 time steps. Omitting the first few iterations serves to avoid the influence of initial transients on the observed signature. On the basis of numerical simulations for smaller chains, one expects the individual spins to approach an almost steady state after initial, short-lived transients. One therefore predicts that most spins would exhibit an exponential decay even for finite ϵ. Because not all the 57 qubits seem to operate within the margins given by the stated error rates, we additionally remove those few ones that deviate substantially from the exponential decay model as judged by convergence of our fit. The above procedure requires us to omit qubits whose error rates are sufficiently high to move their absolute value polarization into the interval [0, The same error mitigation algorithm was applied to all the data in W0 does not crucially affect the results, we process the data using a range of different values. The peak associated with critical fluctuations and the signature of increased damping remain quite stable across a wide range. The same applies to the choice of Wf that enters in the definition of the interval. Here, values very close to 1 produce an algorithm that is too sensitive to fluctuations in the error rates, while values close to 0 suppress the signal. The results presented in this paper were evaluated using W0 = 0.15 and Wf/W0 = 2/3. We find that typically ∼40 to 45 qubits enter the evaluation.To ensure that the arbitrary threshold


It also has the added advantage that it does not require a vacuum pump, and with added laser path improved long term stability but still portable and robust enough to use in everyday applications.Refractive index measurements are required when light is used as the basis of a measurement system. In dimensional metrology, refractive index measurements are used to compensate for the change in the speed of light. This is crucial because the SI unit for the metre is defined as the speed of light in a vacuum. Air refractometers are the most accurate way to measure the speed of light in air. Many research works to date have been performed to measure the refractive index of air using refractometers. This research uses a commercial prism as the vacuum etalon instead of the tube that is used most often. This novelty and newness of our research were to focus on the design, fabrication and testing of a refractometer which uses a permanent vacuum for ease of use but that will still have the same accuracy of other refractometers currently in use. Modifications to existing designs improved the long-term stability compared to other prism refractometers and are also potentially more accurate than tube refractometers. The results achieved with this permanent vacuum refractometer are accurate to 8.4 × 10 In veterinary medicine, it is used to measure the plasma protein and in-cell measurements in biological tissues6. It is also used in the design of optical systems, especially for the medical industry in eye difference design7. Refractive index measurements are also used to determine the sugar content in various beverages, including wine8. The application and impact of refractive index measurements are well captured by Singh9.Refractive index measurements in the medical industry are used to measure, for example, the specific gravity of human urine to determine kidney functionThis paper focuses on refractive index measurements in metrology and more especially dimensional metrology, an area that requires highly accurate measurements. Most measurements are performed at the highest sensitivity for accurate results by utilising laser light to perform the distance measurements. These measurements require the refractive index to be known to a high degree of accuracy.16. However, most dimensional and length measurements are performed in the air. The refractive index in air changes with environmental conditions , and thus, the refractive index of air at the specific conditions must be calculated to make corrections compared to the definition of the metre. This is exacting work and sometimes difficult to achieve practically in the environment.Since 1983, the metre has been defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a secondc, is divided by v′, the velocity of light in air at the time the measurements are taken.To calculate the refractive index, the speed (velocity) of light in a vacuum, n is the refractive index, c is the velocity of light in a vacuum, and v′ is the velocity of light in a particular medium, in this case, air.The refractive index is thus:Many research works to date have been performed to measure the refractive index of air using refractometers. This novelty and newness of our research were to focus on the design, fabrication and testing of a refractometer which uses a permanent vacuum for ease of use but that will still have the same accuracy of other refractometers currently in use. Our device would be suitable for use in everyday applications due to its simplicity of design and ease of use.2) and then calculate it by using equations from Edlin17, Birch18 or Ciddor19. Much research has been done on the differences between these equations by Bonsch and Potulski20 and Kruger and Chetty21. The original calculations were updated specifically for the moisture content of the air. Metrologists in dimensional laboratories and commercial manufacturers of laser measurement systems, such as Rensihaw22, Agilent23 and Zygo24, now mainly use the modified equation. Hence, it was decided to use the modified Edlin equation in this research.The most common method to determine the refractive index is to measure the environmental conditions  is the refractivity of standard air, the temperature T is expressed in degrees Celsius, the air pressure p in torr, standard air at 1 atmosphere and 15 °C.Here  was used to split the two laser beams in the polarising beam splitter. It separates the two beams, f1 and f2, and directs them parallel and 32.62 mm apart23.Figure The vacuum prism was positioned in such a way that the one frequency of the laser, f2, passed through the prism, which is under vacuum and the other frequency, f1, passed above the prism in normal air. With the use of a translation stage, the prism was moved from position 1, the dotted prism, through laser beam f2 to position 2, the solid line prism, thereby replacing the air with a vacuum column.Figure L. The light path in a vacuum, L, is a relative change as the zero position for L is already in a small part of the vacuum.The distance the translation stage is moved, 34, and there was a US patent filed in 1995 by John Tsai35.This method has also been researched by Renkens and Schellekens34, and John Tsai’s35 research was inconclusive because of doubt over whether it had a clear advantage over the tube refractometer. Therefore, the current research investigated whether this method creates an easier to use and more accurate refractometer than the tube refractometer.Renkens and Schellekens21.The angle of the prism together with the distance of travel of the translation stage is needed to calculate the distance of air replaced within a vacuum. From this, the refractive index can be calculated in the same way as the tube refractometerBy substituting Eq.  into 4)4), Eq.  is used 36.The angle of the prism was measured using a Zeiss Prismo Coordinate Measuring Machine (CMM). The accuracy of the CMM measurement is calculated from the CMM specification to be 0.5 µmThe prism intended for liquid refractive index measurements was not ideal for air measurements, and while the angle could be measured accurately, the optical flatness and parallelism of the sides of the prism could not. These measurements are necessary to determine the wavefront of the optical path of the prism while the prism is traversed across the laser beam. To determine this, measurements were taken with air inside the prism. It was assumed that the air inside and outside the prism was at the same temperature, pressure and humidity. These readings were used as a baseline measurement and were added to the final measurements made when there was a vacuum inside the prism.18. In Table 24. The relation between the V.O.L. and the refractive index is shown in Eq. , it did not agree with the weather station method to the same accuracy. The reason was the drift in the zero position. Although the laser beam for the zero position was through a very small amount of vacuum compared to the laser beam through the air, it was enough to drift over time compared with the laser through the air. The drift over a few days was as much as 50 nm between the two laser beams.A new optical layout, Fig. The new optical layout was tested with both laser beams at the zero position over a few days. The difference between the two laser readings was less than the uncertainty in the laser readings.The uncertainty for the Edlin weather station method was calculated by approximating the uncertainty in the measurement for each of the sensors. The uncertainty of the measurements was taken not only from the uncertainty of the calibration but also the accuracy of each sensor during the measurements. This was necessitated by the fact that the sensors are calibrated under near-ideal conditions but the measurements were performed in lesser conditions in the laboratory.–8 in the refractive index; the air humidity uncertainty was estimated to be 2% RH, resulting in an uncertainty of 1.7 × 10–8 in the refractive index; and lastly, the air pressure uncertainty was estimated to be 0.1 mbar, and this resulted in an uncertainty of 2.7 × 10–8 in the refractive index. When combining these uncertainties using the root sum square method, the overall uncertainties from the weather station method were 5.9 × 10–8 in the refractive index37.The uncertainty of the air temperature measurements was estimated to be 0.05 °C, which resulted in an uncertainty of 5.1 × 1036. In Table The uncertainty for the prism refractometer was calculated using Eq. , where tApart from the contributors in the table, the imperfections of the prism faces were calculated by measuring the baseline readings. These measurements were taken in air and added to the readings under vacuum. This eliminated this uncertainty, and only the repeatability in the readings was added to the total uncertainty.–9 in the velocity of light compensation and was not included in this uncertainty budget.However, the deformation of the prism under vacuum had to be included as an uncertainty component. Straightness measurements using the Zeiss CMM were performed under normal environmental conditions with air in the prism at atmospheric conditions. The straightness of the left side of the prism is shown in Fig. 37 is 8.4 × 10–8 in the measurement of the refractive index.The combined uncertainties using the root sum square method–7 with the Edlin weather station method for the short travel and better than 8.4 × 10–9 for the longer travel of the transverse stage.The aim of this research was to investigate the use of a permanent vacuum hollow prism as the vacuum etalon in an air refractometer in order to eliminate the use of a vacuum pump during refractive index measurements. The results of the translation showed an agreement of 1.82 × 1020. This is due to the optics being under the same conditions during the entire measurement. This is a great improvement in the potential accuracy of prism refractometers over tube refractometers.The use of a prism as the vacuum etalon further eliminated the difficulties due to the change of the optical length of the side windows of a tube refractometer as describe by Bonsch and Potulski34, and John Tsai’s35. This design can now be used for a prolonged period after the prism had been translated and kept at the 25 mm position, which is a big improvement over previous designs. With these improvements, the refractometer proved advantageous not only for refractive index air measurements in dimensional metrology on a daily basis but also for high accurate research.Adding an extra set of laser beams to the prism refractometer improved the long-term accuracy of the refractometer, compared to other prism refractometers as describe by Renkens and SchellekensFuture improvements to the system will focus on the commercial prism. The side windows of the prism should be manufactured of better-quality optical material and to a higher accuracy in flatness and parallelism to increase the overall accuracy of the system.The results, both in everyday use for long-term measurements and highly accurate research, prove the original objective of this research.


In most cascading failure models in networks, overloaded nodes are assumed to fail and are removed from the network. However, this is not always the case due to network mitigation measures. Considering the effects of these mitigating measures, we propose a new cascading failure model that describes the probability that an overloaded node fails as a logistic function. By performing numerical simulations of cascading failures on Barabási and Albert (BA) scale-free networks and a real airport network, we compare the results of our model and the established model describing the probability of failure as a linear function. The simulation results show that the difference in the robustness of the two models depends on the initial load distribution and the redistribution of load. We further investigate the conditions of our new model under which the network exhibits the strongest robustness in terms of the load distribution and the network topology. We find the optimal value for the parameter of the load distribution and demonstrate that the robustness of the network improves as the average degree increases. The results regarding the optimal load distribution are verified by theoretical analysis. This work can be used to develop effective mitigation measures and design networks that are robust to cascading failure phenomena. Therefore, given the increasing complexity of the networks that our daily lives largely depend on, the exploration of cascading failures in network context is fundamental to understanding and controlling them. To this end, developing a universal model that can characterize cascading failures in complex networks is essential.Many networks, including infrastructure networks such as electrical power grids, communications systems, and transportation networks, function through strong interactions between components. This interconnectedness suggests that any malfunction of one or several nodes due to random failures or targeted attacks can propagate through the entire system and thus cause system failures. Examples of the widespread impact of these cascading failures include the Western North American blackouts in 19967, including betweeness centrality model10, Motter-Lai model12, and effective efficiency model13. In addition, many studies have been conducted focusing on defense strategies against cascading failures16 and improving the robustness of networks19. In most cascading failure models, the node of a network is assumed to fail when its load exceeds its capacity. In other words, the probability that a node fails is 0 when the load is smaller than the capacity and 1 when the load is larger than the capacity. If we plot this probability as a function of load, we obtain a Heaviside step function translated by the value of the capacity in the positive load direction. The overloaded node, however, does not necessarily fail and cease to function because most networks have some mitigation measures that allow overloaded nodes to continue functioning. For instance, it has been argued that overloaded power lines do not immediately break down20.Various approaches have been proposed to describe cascading failures in complex networks21. Subsequently, a modified model based on the removal threshold has also been proposed22. According to the study by Wang et al21, the breakdown probability, which is the probability that a node fails , is as follows: 0 for the range where the load is less than the capacity, 1 for the range where the load is greater than the removal threshold, and between 0 and 1 when the load is greater than the capacity and less than the removal threshold. They further assumed that the probability of failure is linearly proportional to its load when the load is in the range between the capacity and the removal threshold  as showentclass1pt{minimaentclass1pt{minimaentclass1pt{minima21. They assume that 32 suggested that the cost w of preventing cascading failures in a network can be defined asThe value of entclass1pt{minimaj in Eq.  is \docuj in Eq. . Eq. 6)\documententclass1pt{minimaentclass1pt{minima28 where From the entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaAs can be seen in Figs. entclass1pt{minima1.0 Fig. a whereas1.0 Fig. c. For \dres Fig. b.Figure To examine the effect of network topology on the robustness of networks in our logistic model, we also ran the simulations in scale-free networks with diverse average degrees. In Fig. 24. Figure To apply our model to real networks, we also simulated cascading failures in the US airport network as of 1997 where nodes represent airports, and a link connects between two airports when there is a direct flight between them i is terminated. The conditions that the neighboring node j of node i should satisfy for p is the random number between 0 and 1. If we substitute Eq. (i with the degree p, thus, we calculate p in Eq. (p is the random number between 0 and 1, its expectation value is 0.5. Replacing p in Eq. (To validate the numerical results from the previous section, we examine our cascading failure model theoretically. Our purpose of theoretical analysis is to find the value of mentclass2pt{minimmentclass2pt{minim and Eq.  for \docmentclasspt{minimap by their expectation values, To find the value of 1 in Eq.  as15\docfrom Eq.  and the 1 in Eq.  can be mwith Eq.  indicateentclass1pt{minimaentclass1pt{minimaWe have presented a new cascading failure model by modeling the probability of failure of an overloaded node as a logistic function. The probability of failure is adopted to consider the effects of mitigation measures of the network. Then we focus on the nonlinear relationship between the probability of failure and the load on the node and introduce a logistic function to characterize it. We have performed numerical simulations of cascading failures on BA networks and a real airport network to investigate the cascading behaviors of our model.The proposed probability of failure improves the robustness of the network compared to the case where the probability of failure is not adopted as expected. To assess the efficiency of our cascading failure model in improving the robustness of the network, we compare the results of our logistic model with those of the linear model. We have found that the comparison results of the robustness using the two models depend on the way the load is initially assigned on the node and redistributed between nodes. The conditions that enhance a network’s robustness were also examined regarding the load distribution and the topology of the network. The optimal value for the parameter of the load distribution has been found, and is also investigated by theoretical analysis. In terms of the topology of the network, the network becomes more robust as the average degree of the network increases.The main objective of our study is to introduce a new cascading failure model and to investigate its behavior and efficiency in improving the robustness of the network. We used BA network as a model system since BA networks can represent many natural and artificial systems. Therefore, the results of this study can be used to analyze cascading failure events in real systems. The main findings of our study is that the results of comparison between logistic and linear probabilities of failure depend on the initial load distribution and the redistribution of load. This can be used to devise effective anti-impact strategies against cascading failures in complex networks.


Visual salience is a key component of attentional selection, the process that guards the scarce resources needed for conscious recognition and perception. In previous works, we proposed a measure of visual salience based on a formal theory of visual selection. However, the strength of visual salience depends on the time course as well as local physical contrasts. Evidence from multiple experimental designs in the literature suggests that the strength of salience rises initially and declines after approximately 150 ms. The present article amends the theory-based salience measure beyond local physical contrasts to the time course of salience. It does so through a first experiment which reveals that—contrary to expectations—salience is not reduced during the first 150 ms after onset. Instead, the overall visual processing capacity is severely reduced, which corresponds to a reduced processing speed of all stimuli in the visual field. A second experiment confirms this conclusion by replicating the result. We argue that the slower stimulus processing may have been overlooked previously because the attentional selection mechanism had not yet been modeled in studies on the time course of salience. Physical contrasts like these that stand out from their surroundings are referred to as salience . Both events are separated by a brief interval, the stimulus onset asynchrony (SOA). This accuracy-based task requires a binary decision (“A before B” or “B before A”). The task is related to attention because of the phenomenon that an attended stimulus is perceived earlier than an otherwise similar but unattended stimulus. Attention thus leads to a systematic deviation of the reported from the objectively correct order  and the just noticeable difference (JND)  of 50, 100, 200, 400, or 800 ms before the probe and reference stimuli flickered. The display persisted until the end of the trial—only the length of the visibility prior to the TOJ was varied. The only change to the display was the brief flicker of the probe and reference stimulus. The flicker was implemented by an offset and subsequent onset, that is, the stimulus disappeared for 80 ms. The order in which the two stimuli flickered depended on an SOA of Instructions were presented on the screen and questions were answered by the experimenter verbally.The participants were instructed to look at the fixation cross as soon as it became visible at the beginning of each trial. Participants then had to judge which of two flicker events was the first and respond by indicating the respective side: left or right. The response was given by pressing the left ctrl or the right enter key with the respective hand. A new trial started automatically, but breaks were offered after 50 trials. The experiment began with a training session of 40 trials. During this training, feedback about the correctness of the participant’s judgments was given. The locations of the relevant events were learned as well as the task in general. The whole session lasted approximately 45 min.C.Applying the model derived from TVA, two parameters are estimated from the TOJ data for each of the five experimental conditions. A Bayesian hierarchical model is used to represent different sources of uncertainty  according to the logic of the experimental design. The parameter estimations for the population are shown in Figs.  d, The similarity of two groups can be assessed by comparing their parameter distributions: The smaller their overlap, the larger the effect. To provide an objective assessment of the difference of two conditions, we compute the standardized effect size (Cohen’sC depict different patterns. The salience parameter The figures for salience C rises steeply during the first 200 ms. The non-overlapping posterior distributions suggest that the 50 ms and 100 ms conditions are profoundly different from each other. This is again substantiated by the first two effect sizes that fall completely outside the ROPE. The estimated effect sizes are 0.86  for Condition DOA 100 ms and DOA 50 ms, 1  for Condition DOA 200 ms and DOA 100 ms, C reaches the expected value only after 200 ms but appears to be constant from there on.Although hypothesized to be constant, the processing capacity C model. We use the leave-one-out Information Criterion (looIC; Vehtari, Gelman & Gabry, C exhibits a time course. Fixing the C parameter however results in a worse model than fixing k. Thus, we can conclude that a time course of salience exists, although the time course of C is more important for the observed data pattern.According to the hypothesis, the Next, we compare the present model to an alternative that replaces the TVA-based psychometric function with the logistic function while retaining the same hierarchical structure. Again, we use looIC for comparison. This procedure yields an looIC of 3896.31 for the original model and an looIC of 3924.89 for the logistic function model. Priors for the logistic function model are taken from a study by Krüger et al.  who provC determines how steep the TOJ curve is, whereas Although the analysis shows that assuming no change in the salience parameter Previous studies on the time course of salience used a blocked design (e.g. , Dombrowe et al., To sum up, we applied a model derived from a theory of visual selection, the TVA, to an experimental design, the TOJ, that is used to investigate the time course of visual salience. However, the overall ability to perform the TOJ, measured by the visual processing capacity, exhibits a stronger time course than the salience parameter. This result contradicts the hypothesis that only the distribution of attention caused by salience is affected by a time course. This finding does not originate from applying an inappropriate model to the data. This cause has been ruled out by a model comparison between the TVA-based model and a model that uses the common logistic function instead of the function derived from TVA. Thus, from the TVA perspective, there is rather a time course in the accuracy of the TOJ than in the relative advantage of the salient over the non-salient stimulus. To preclude the possibility of a chance finding or a biased parameter estimation because of temporal expectancy, we conducted a blocked replication study in Experiment 2.C in Experiment 2 with blocked conditions. A blocked design makes the experiment more comparable to previous studies on the time course of salience that used blocked designs (e.g. Dombrowe et al., Experiment 2 was conducted to replicate the findings on processing capacity Thirty persons (9 male and 21 female; a Krüger .The same apparatus as in Experiment 1 was used.Stimuli were the same as in Experiment 1.The procedure was the same as in Experiment 1 except that the DOA conditions appeared blocked. The order of blocks was randomized.The estimated salience value, C between the first three levels of DOA. The exact estimates for the capacity effect sizes are 1.1  for Condition DOA 100 ms and DOA 50 ms, 0.95  for Condition DOA 200 ms and DOA 100 ms, The testing for medium or larger effects for two consecutive levels of DOA shows the same result: There is a medium or larger effect for C model, 4781.35, shows the same order as in Experiment 1: The parameter C varies more distinctly between conditions. Also, the TVA-based model was, as in Experiment 1, compared to a model using the logistic function as psychometric function while preserving the same structure. The two models were compared by looIC. This comparison yielded 3831.49 for the original and 3848.23 for the logistic function model. As in Experiment 1, this comparison stresses the point that the TVA-based model provides a good description of the data.Comparing the looIC of the original model, 3831.49, against the fixed-The parameter C. After the successful replication of Experiment 1, it is appropriate to interpret this distinct pattern, which corresponds to reduced resources for the task in general, when the DOA is smaller than 200 ms. One explanation of a changing processing capacity may be alertness. TVA research shows that an alerting stimulus preceding the task-relevant stimuli may indeed affect processing capacity. However, processing capacity has been reported to increase under these circumstances (Matthias et al., Nevertheless, the clearest evidence for a time course was again found in the overall processing capacity C because a decrease in processing capacity C corresponds to a decreased performance in the temporal judgment.Beyond the TVA literature, Yeshurun & Levy  report tHowever, Experiment 1 and Experiment 2 were not designed to test how TVA parameters relate to specific or even conflicting neurophysiological or behavioral findings beyond the recurrent patterns in the time course of salience. Thus, the main contribution of Experiment 2 is that the original findings have been successfully replicated. That is, a model derived from TVA to provide a quantitative measure of visual salience can also capture the time course of salience in theoretically interpretable variables. This model revealed a time course in the general performance of judging temporal order as well as in the relative advantage of the salient stimulus.C. The resulting two-parameter model links data and theory mathematically: The numerical values of salience and overall processing capacity are, on the one hand, statistically inferred from the observed data. On the other hand, these two parameters have a specific theoretical meaning in a formal theory of visual attention. The present modeling and empirical approach yields a common salience measure that quantifies the effect of time course on visual salience.Previous studies show that the effect of visual salience on attention depends on a time course as well as physical contrast. We formally quantified the strength of salience by modeling the relationship between salience, attention and visual selection based on a theory of visual selection: Bundesen’s TVA (for the measurement of physical contrasts see Krüger et al., C shows medium or large effects for consecutive DOA levels in the range up to 200 ms. This pattern means that temporal discrimination performance is strongly reduced for short display durations. Because such a pattern was not part of the hypothesis in Experiment 1, we conducted a replication in Experiment 2 which confirmed the finding.In the empirical part of this article, the two-parameter model-based analysis revealed that salience is highest after 50 ms and changes over time, which was checked by a model comparison to a model assuming a fixed Before the results of these parameter estimations are compared to previous research on the time course of visual salience, it is useful to take one step back and discuss the model. Formal modeling has often been advocated as important particularly for linking theory and data (e.g., Rouder, Morey & Wagenmakers, TVA models visual selection and attention based on the simple yet evocative concept of biased competition (Desimone & Duncan, The specific meaning of TVA’s salience parameter allows theorizing about stimulus-driven attention beyond the TOJ design. The salience parameter was developed from a partial-report design (Nordfang et al., To sum up our model evaluation, the model provides a good fit to the TOJ data and contributes to the integration of salience and TVA research. We hope that the reader is inclined to entertain the presented model as a useful way of looking at attentional influences of salience in TOJ as modeled by TVA so that the parameter values can be understood as representative of the properties of cognitive processes.The salience parameter estimation provides an estimation of the time course of salience. Whereas the literature agrees that a time course of salience exists, there is discord about its shape. The different shapes of the time course have been reviewed in the introduction to form the original hypothesis. The reviewed time courses can be summarized in two points: First, does the effect of salience on attention increase during the presentation duration up until 200 ms (e.g., Dombrowe et al., It is important to note that our evaluation of the strength of salience works exclusively through the surrogate of attention. An operationalization using perception (e.g., Nothdurft, It is not optimal that one SOA is missing in the 50 ms DOA condition. However, in comparison to our earlier works, we already reduced the SOA from a maximum of 100 ms to 80 ms to be able to use all SOAs in the 100 ms DOA condition. Balanced SOAs for the 50 ms DOA condition were not possible. Yet, we wanted to include this condition because DOAs in this region have been used in the literature before. Note that the Bayesian analysis accounts for the reduced amount of data in the 100 ms DOA condition. This results in wider posterior distributions, if everything else is kept constant. Therefore, the narrow parameter distribution for this condition must originate from less variance in the available data. Yet, we cannot exclude the possibility of a bias in this condition caused by the unbalanced design. However, if the 50 ms DOA condition were removed altogether, the conclusion would still hold because of the 100 ms DOA condition’s difference to the longer DOA conditions.Another limiting factor of the study is that some of TVA’s attentional parameters cannot be estimated: As of yet, it is not possible to derive the minimum effective exposure duration, Despite its limitations, our theory-based approach made a specific prediction of how salience should affect the data, which we illustrated for the salience parameter and for the overall processing capacity in Fig. Within the scope of this article, we cannot investigate whether or not only temporal discrimination performance is reduced until 200 ms after the onset of the salience display. Peripheral cues have been reported to diminish temporal discrimination performance (Yeshurun & Levy, C in the TVA based model, see Fig. Low C values for the short DOA conditions might be an artifact caused by the flicker. At least presentation duration and perceived offset are negatively proportional in the range used (Coltheart, A model-based salience measure does not come without its caveats: Because TVA-designs are accuracy-based, it is difficult to relate the estimated salience value to salience research using speeded responses. One way of reconciling these lines of research is by referring to TVA models that also model response times (Kyllingsbæk, Markussen & Bundesen, To sum up, we measured the time course of salience successfully with a model derived from a theory of visual selection, TVA. We further showed that the model adequately describes the observed data by a comparison to a common psychometric model. This analysis revealed that salience decreases over time but remains an influence on attention even after 800 ms. However, the performance in the TOJ was much worse for short display durations of 50 ms and 100 ms. This effect is captured by overall processing capacity. Thus, the salience measure requires accepting basic TVA modeling but enables researchers to sharpen the concept of visual salience by differentiating actual influences on salience from possible confounds.


Tropical deep convection can aggregate into large clusters, which can have impacts on the local humidity and precipitation. Sea surface temperature (SST) gradients have been shown to organize convection, yet there has been little work done to investigate the impact of diabatic heating perturbations in the atmosphere on the aggregation of convection. Here we investigate how anomalous diabatic heating of the atmospheric column, through an idealized aerosol plume, affects the existence and mechanisms of convective aggregation in non‐rotating, global radiative‐convective equilibrium simulations. We show that the aerosol forcing has the ability to increase the degree of aggregation, especially at lower SSTs. Detailed investigation shows that the diabatic heating source incites a thermally driven circulation, forced by the shortwave perturbation. The increase in aggregation is caused in part by this circulation, and in part by the longwave heating anomalies occurring due to the surface convergence of moisture and convection. At higher SSTs, longwave feedbacks are crucial for the aggregation of convection, even with the shortwave heating perturbation. At lower SSTs, convection is able to aggregate with the shortwave perturbation in the absence of longwave feedbacks. These perturbations provide a link to studying the effects of absorbing aerosol plumes on convection, for example during the Indian monsoon season. We argue that, as there is aggregation for plumes with realistic aerosol absorption optical depths, this could be an analogue for real‐world organization in regions with high pollution. Can increase the degree of aggregation by using a shortwave radiative heating perturbationRadiative heating perturbation incites a global thermally driven circulationShortwave radiative heating perturbation can aggregate convection at lower sea surface temperatures, even without typically crucial longwave feedbacks Convection can be defined as organized when multiple convective cores group together to form large clusters. Convective organization can take many forms, such as squall lines, mesoscale convective systems or supercell clusters  setup. RCE is the equilibrium state the atmosphere would reach in the absence of lateral energy transport. In this state, the equilibrium is reached by a balance between the convective and radiative processes  however the link between the simulated and observed aggregation remains unclear and is one of the key questions in the study of convective self‐aggregation. Many of the processes organizing the convection in these idealized studies are exhibited on a much larger scale in the formation of the Madden‐Julien Oscillation (MJO)  Atmospheric GCM  model  . Therefore, the aerosol plume does not generate convective aggregation that exhibits hysteresis, and the existence of the cluster is directly linked to the existence of the forcing.Many previous studies of convective self‐aggregation have found the convective cluster to exhibit hysteresis ‐ that is, once it has aggregated it will remain so even if the necessary feedbacks are removed , which is defined asTherefore, the values of AAOD tested were 0.06, 0.08, 0.1, 0.12, 0.2, 0.24, and 0.36.σCRH2. When the AAOD is increased to 0.12 or greater there are significant increases in σCRH2 and therefore, increases in the degree of aggregation. The simulations with an aerosol plume AAOD of 0.24 and 0.36 show the strongest response, with the simulations with an AAOD of 0.12, and 0.2 also showing an increase in σCRH2 compared with the simulation without an aerosol plume. From this, we note that, for the aerosol plume to have an impact on the aggregation convection at an SST of 290K, there must be an AAOD of at least 0.12. Pollution plumes seen in the real‐world can have AAODs of 0.12 or greater during high pollution events, such as the during biomass burning events . It is hypothesized that the strongly positive feedback in the simulation with the plume is due to increased windspeed due to the increased convergence driven by the plume. This is the positive WISHE mechanism described in Coppin and Bony . For the4.1.1The key positive feedback behind the longwave mechanism in these simulations is the strong longwave warming in the boundary layer below the clouds, combined with the low emission temperatures at the top of the deep convective clouds. This causes a strong temperature gradient, driving a humidity gradient and an upgradient transport of FMSE. The cloud driven feedback is the same as the longwave maintenance feedback described in Wing and Emanuel .4.1.2h^, and so we see a positive shortwave feedback everywhere in the domain. The increased contributions from the shortwave feedbacks in the wettest columns in the run at 290K SST with the plume arise from the direct shortwave absorption associated with the plume. This strong shortwave perturbation, also seen in Figure The small, but positive, shortwave feedbacks in the plume‐free runs are simple to understand: as water vapor is an absorber in the shortwave, wet columns will have higher absorption than the drier columns. This correlates well with the anomalies of 4.2To further investigate the role longwave and shortwave feedbacks play with and without the plume in our simulations, we ran a suite of experiments where the longwave and shortwave fluxes were homogenized in turn at each timestep, and at each model layer, following Muller and Held . ShamekhIn this section, we describe simulations by SST_plume_homogenization, so the experiment at 290K SST, without a plume and with longwave fluxes homogenized would be called 290K_homogLW, and the run with the same SST and homogenization but with the plume would be called 290K_plume_homogLW. We also note that the 290K_plume_homogLW experiment has a plume with AOD = 1, and the 305K_plume_homogLW experiment has a plume with AOD = 0.8, compared to the plume with AOD = 1.8 used in the rest of the simulations. However, testing has shown that a plume of this shape and size, with SSA = 0.8, can force an increase in the degree of aggregation at AODs of 0.6 or greater. Also, these two simulations homogenize the longwave fluxes for three out of every four timesteps. Whilst this does not fully homogenize the longwave heating field, we have seen that this amount of homogenizing is sufficient to decrease the degree of aggregation to close to the value in our control runs (not shown). These measures are taken to ensure that the model stays in equilibrium as using high AOD and fully homogenizing the longwave heating leads to excessive instabilities.4.2.1σCRH2, for runs with fully interactive fluxes and homogenized longwave fluxes. It is clear, from Figure Figure σCRH2.When shortwave fluxes are homogenized, there is little visible difference in how aggregated the moisture field is. Indeed, when the degree of aggregation is compared in Figure 4.2.2When shortwave fluxes are homogenized with the plume in the simulations, the moisture distribution returns to roughly how it was arranged with no plume. This makes intuitive sense, as our plume model works by perturbing the shortwave absorption. When these perturbations are then homogenized across the domain, we will no longer see spatial evidence of the plume. We can see this in Figures The key remaining question, is whether the shortwave perturbations induced by the plume generate a powerful enough circulation to force convection to aggregate without interactive longwave fluxes. From the evidence provided in Section To fully understand why the shortwave feedbacks are more effective at aggregating the convection at 290K SST with the plume (compared to 305K SST) we investigate the differences in the absolute magnitude of the circulation and radiative heating perturbations induced by the plume when longwave fluxes are homogenized Figure . At both5Convective self‐aggregation has been shown to occur in many different modeling setups, including in general circulation models (GCMs) with a convective parameterization scheme. Work thus far has focused on spontaneously occurring self‐aggregation. In this study, we focus on convective aggregation in the presence of an external source of diabatic heating, representative of aerosol radiative perturbations. This plume induces a thermally driven circulation. We were particularly interested in how the forcing affected the ability of a simulation to aggregate, and whether the mechanisms behind this forced aggregation differ from those causing a spontaneous self‐aggregation.The radiative perturbation caused by the aerosol plume forces an increase in the degree of aggregation through the generation of a large‐scale circulation. This circulation is driven by strong shortwave warming due to the aerosol absorption, and enhanced by strong boundary layer longwave warming from the aggregation of moisture. The aggregation that is forced by this radiative plume is a superposition of two circulations. One circulation has radial convergence toward the plume in the lower atmosphere and radial divergence in the upper atmosphere. The second circulation works tangentially to the plume again with lower‐level convergence and upper‐level divergence, shaping the lines of convection connected radially to the central cluster formed around the plume.The forced aggregation shown in this study is dependent on the aerosol plume. When the plume was removed, the convection immediately disaggregates. Therefore, in contrast to previous studies  of 0.12 or greater is required to force simulations to aggregate at an SST of 290K, and the maximum degree of aggregation is reached at an AAOD of roughly 0.24. There are many examples of aerosol plumes with AAODs greater than 0.12 in the real world such as pollution, dust events, and biomass burning events (e.g., Eck et al.,


The study of changes in species richness and composition along rivers has focused on large spatial scales. It has been ignored that in different sections of the river  the specific environmental conditions can generate different longitudinal patterns of the species richness and composition. In this study, we determine whether species richness and composition of the riparian plant communities change along a mountain river and whether these changes are related to environmental variables. We expect an increase in species richness and turnover along the river, that the upstream communities would be a subset of the downstream communities, and that such would be related to edaphic and hydrologic conditions. To test this, we sampled three strata of the riparian vegetation  in a set of 15 sites that we place along a mountain river. Additionally, we recorded topographic, hydrological, morphological, and soil variables. We performed correlation analyzes to determine whether changes in species richness and turnover were related to increased distance to the origin of the river. Also, we obtained the nestedness and evaluated the importance of environmental variables with GLM, LASSO regression, and CCA. With the increase in distance, the species richness decreases in the upper stratum, but not in the middle and the low stratum , the turnover increase in all strata and the upstream communities were not a subset of the downstream communities. The changes in species richness and composition were related to topographic , hydrological (flow), and edaphic (conductivity and pH) variables. Our results indicate that at small spatial scales the patterns of richness and composition differ from what has been found at larger spatial scales and that these patterns are associated with environmental changes in the strong altitude gradients of mountain rivers. Along the rivers, it is possible to observe patterns in the diversity of plants. We find that in mountain rivers the species richness decreases; there is an increase in the turnover and absence of nesting of the communities along the rivers. These patterns of diversity are determined by altitudinal contrasts and changes in hydrological and edaphological characteristics that contrast with what has been found in previous works. We expected that (a) species richness increases with distance to the origin of the river; that there are changes in the composition, (b) specifically that the turnover of species increases with distance from the origin of river, and (c) that upstream community composition constitutes a subset of the species found in downstream communities; finally, we expected that (d) changes in species richness and composition will be associated with changes in edaphic and hydrologic conditions in the riparian zones.22.1Abies hickelii forests and Pinus hartwegii forests in the highest zone and mixed forests of A. hickelli‐Pinus patula and of Pinus pseudostrobus var. apulcensis‐Quercus crassifolia toward the zones medium and low  Figure . In orde2.32 (3x33.3 m). For the middle stratum, all the individuals smaller than 1 cm of ND were measured in two plots of 50 m2 (2x25 m). Finally, for the lower stratum, the coverage of all individuals <1 m tall were recorded in two plots of 1 m2 (1 × 1 m).Fieldwork was carried out during the two seasons with the greatest floristic contrast in the area (dry season = March 2017 and rainy season = November 2017). To floristically characterize the riparian communities that develop along the river, at each sampling site all vascular plant species were recorded in plots of different sizes depending on the stratum studied; in each parcel, all individuals per species (except for low stratum) and his normalized diameter (ND = diameter at height of 1.3 m) were registered. Due to the rugged topography of the area, the plots were placed on a riverbank. The strata were separated because different life forms dominated the upper and middle layers (dominated by trees and shrubs) and the lower layer (dominated by herbaceous plants). For the upper stratum, all individuals with more than 1 cm of ND were measured in two plots of ~ 100 m2.4We selected a set of sites covering the distance gradient to the river origin  as well as the prevailing climatic and soil conditions in the area to analyze whether changes in species richness and composition were related to changes in environmental variables. At each of these sites, we recorded altitude as well as morphological, hydrological, and edaphological variables. For recording environmental variables, the sites were visited on four occasions between March and November 2017, except for flow, which was only recorded in the rainy season (November 2017). For the morphological variables, we obtained the average channel width at each site by measuring the distance between the growth lines of the vegetation on both banks of the river at three sites.Q = V/kΔt∑n[EC(t)–ECbg]. Where Q is flow, k is the calibration constant, t is any time during the registration of the chemical marker, EC(t) is the electrical conductivity measured in time t, and ECbg is the initial electrical conductivity of the river. In the field, all EC measurements were taken at a constant distance at all sites (20 m to the dumping site). The volume of NaCl varies depending on the size of the river . The length of time the EC measurements lasted depended on the speed at which the entire volume of the chemical marker discharged into the river passed the measurement point at each site . These measurements of the river flow were made once in the rainy season.Regarding the hydrological variable, was calculated the river flow at each of the sample sites using the salt hit method. This method consists of the use of a chemical marker (NaCl) that allows the recording of changes in electrical conductivity (EC) in the water from the river through time. With these measurements, we subsequently calculate the flow using the formula Moore, : Q = V/kFor the edaphic characterization of the riparian zone, soil measurements of electrical conductivity, moisture content, pH, and temperature were recorded with a multiparameter and an electronic sensor throughout one year Figure . For the2.5All the analysis was made for each stratum with the help of the R ver. 3.5.2 software . Rarefaction allows the direct comparison of diversity values between differently sampled sites by calculating an expected number of species based on fixed sample size , a Spearman correlation analysis was performed to determine whether the changes in species richness were related to the increase in the distance to the origin site of the river.For species richness, the R‐package iNext was used to perform rarefaction analysis and calculated the Hill number of order 0  as a measure of replacement and a matrix with transformed environmental variables (log) to obtain the Euclidean distance between sites as a measure of environmental dissimilarity in the distance gradient. Simpson's dissimilarity coefficient was used because this index accounts only for turnover between communities /2]+[m(m–1)/2]. Where Npaired is a degree of paired nestednesss, n(n–1)/2 and m(m–1)/2 is the degree of nestedness for n columns (species) and m (sites) rows, respectively. The NODF takes values ranging from 0 to 100, a value of 100 indicates total nestedness of the communities . For the low stratum, the RIV was obtained with: RIV= ∑RFi+∑RDi/2.The species relative importance value (RIV) was obtained for each site. The RIV is a comprehensive indicator that used to determine the overall importance of each species in the community structure  were used to evaluate the relationship between species richness and composition of plant communities with environmental variables. To avoid collinearity between the environmental variables, a Pearson correlation analysis was performed with the variables transformed on a logarithmic scale Appendix . Three eWe used GLMs  to test whether there was a relationship between environmental variables and species richness. The GLMs were made with R‐package lme4 . The CCA is an ordination technique that evaluates the associations between a set of environmental variables and the response variable, in this case, data on the composition of communities . For the middle stratum, we did not observe a significant relationship between the species richness and the position of the sites in the river . For the low stratum, we also do not observe a significant relationship between the species richness and the position of the sites in the river  . We detected a negative and significant correlation between the species richness and the distance to the origin of the river for the upper stratum  but not in the middle  and in the low stratum . The results show that with the increase in the geographical distance between sites, the differences in environmental conditions increase .With the increase in environmental dissimilarity, the turnover of species in the upper stratum increases  and for the low stratum  but not in the middle stratum . The lowest turnover values for all strata were observed between the closest sites   and for the low stratum  but not in the middle stratum . The highest nestedness values for all strata were observed between the closest sites .   had the highest RIV values in the sites where they were observed . For this stratum, in the LASSO regression three variables were maintained, the most important being conductivity. In the middle stratum, both the GLMs and the Lasso regression indicate that was significantly positively related to pH. In the low stratum, the species richness was significantly negatively related to the interaction of altitude with flow, in this stratum hierarchical partitioning identified flow as the most important variable (55.42% of the variance explained), a similar result was obtained with the LASSO regression Tables  and 2.r = 0.93) and negatively with the altitude (r= −0.97). In axis 2 (explained variance = 27.9%), it was correlated positively with the conductivity (r = 0.43). For the middle stratum, the CCA indicated that the first two axes of ordination explained 48.7% of the variation of the floristic composition that we observe along the river  and negatively with the altitude (r= −0.84). In axis 2 (explained variance = 22.9%), it was positively correlated with the conductivity (r = 0.82) and negatively correlated with pH (r = 0.73). For the low stratum, the CCA indicated that the first two axes of ordination explained 48.1% of the variation of the floristic composition that we observe along the river  and negatively with the altitude (r = 0.76). In axis 2 (explained variance = 23.5%), it was positively correlated with pH (r = 0.57).Finally, the CCA indicates that the first two axes explained 61.3% of the variation of the floristic composition of the upper stratum along the river Figure  a. In axr Figure  b. In axr Figure  b. In ax4Different from our expectation, we found a negative relationship between species richness and distance to the origin of the river as well as that the nestedness component was not predominant; as such, we found no support for the "River Collector Hypothesis" (RCH)  along the river are related to changes in the diversity of riparian plant communities that develop in mountain rivers, we could not rule out a possible effect of propagule dispersal, since we do not include propagule dispersal as an explanatory variable. We establish two possible hypotheses by which the propagule dispersal process did not determine the patterns of diversity, according to the theoretical framework of the HRC and our hypotheses: (a) along a mountain river there is no greater deposition of propagules in the riparian zones with the increase in the distance to the site of origin of the river, because the erosive capacity exceeds that of deposition, so that the propagules that are transported in the body of water are not deposited in the riparian zone, on the other hand, if they are deposited they are quickly removed by the water flow to downstream riparian zones that develop outside the mountain area and (b) the propagules are effectively transported and deposited in the riparian zones, but environmental filters do not allow their germination or establishment because they do not have the mechanisms to stay in place.Another aspect to consider is the environmental changes throughout the year since differences were observed in the edaphic variables of conductivity and moisture. These are related to changes in precipitation between the dry and the rainy season, which modify the water level in rivers and with it the conductivity and moisture in the riparian zone  and the confounding effect that it may have generated in the variables that were found to be most important for the changes we observed in the riparian communities. Three key problems arise under collinearity: (a) reverse interpretation (the estimated coefficients have the wrong sign), (b) suppression or masking , and (c) dangerous extrapolation  ; Data curation (lead); Formal analysis (lead); Methodology ; Validation (lead); Writing‐original draft (lead); Writing‐review & editing (lead). Trejo Irma: Funding acquisition (lead); Methodology ; Resources (lead); Supervision ; Writing‐review & editing (lead). Neptalí Ramírez‐Marcial: Methodology ; Supervision ; Writing‐review & editing (supporting).Supplementary MaterialClick here for additional data file.


Resistive switching is an important phenomenon for future memory devices such as resistance random access memories or neuronal networks. While there are different types of resistive switching, such as filament or interface switching, this work focuses on bulk switching in amorphous, binary oxides. Bulk switching was found experimentally in different oxides, for example in amorphous gallium oxide. The forms of the observed current–voltage curves differ, however, fundamentally. Even within the same material, both abnormal bipolar and normal bipolar resistive switching were found. Here, we use a new drift–diffusion model to theoretically investigate bulk switching in amorphous oxides where the electronic conductivity can be described by Mott’s concept of a mobility edge. We show not only that a strong, non-linear dependence of the electronic conductivity on the oxygen content is necessary for bulk switching but also that changing the geometry of the memristive device causes the transition between abnormal and normal bipolar switching. In this context, memristive devices got attentionfor their use as resistance random access memories (ReRAM) or for neuronal networks. Depending on the preceded voltage, the memristive device can be switched between two states, a high resistive state (HRS) and a low resistive state (LRS)3. Several experimental investigations have shown that gallium oxide and especially amorphous, substoichiometric gallium oxide thin films  maximum and the conduction band (CB) minimum are not as clearly defined as in crystalline solids I–V curveial Eqs. –10) and andI–V cial Eqs. –20) and andI–V cI–V curve is reached, i.e. the following curves are identical. From now on, all I–V curves are steady I–V curves.Because of the homogeneous starting configuration for the oxygen ions, the first cycle is notably different from the subsequent ones, while after the third cycle a steady I–V curve  and can be calculated by Eq.  there is again no significant polarisation resulting in ohmic behaviour. Our results are in agreement with the results from Kalaev et al.34.In Fig. I–V curves for the variation of the sample’s thickness are shown in Fig. I–V curves show more pronounced switching behaviour. Additionally, the sample’s thickness influences the gradient of the electrochemical potential of the electrons The I–V curve is the same for all compositions, but the slope depends strongly on the oxygen content and the connected concentration of electrons. The inset in Fig. The influence of the initial stoichiometry is shown in Fig. 35 and a voltage of 6 we still observe pronounced abnormal bipolar resistive switching. The corresponding current–voltage curve is shown in Fig. I–V curve which is only reached after about 20 cycles.Before we moved to quasi three-dimensional simulations, we performed additional 1D simulations to make sure that they also work with lower diffusion coefficients and higher voltages. With a diffusion coefficient for the oxygen ions of In a three-dimensional model, the variation of the TE-area to BE-area ratio is now possible. We performed the simulations in a 2D rotationally symmetric model, which is quasi 3D, in order to save computational time.I–V curves for the variation of the size of the bottom electrode while the size of the top electrode is constant.Figure I–V curve  the switching behaviour has changed to normal counter-8 bipolar switching. Both the abnormal bipolar behaviour8 and the normal bipolar behaviour6 have been found experimentally, but without any connection between them. Here, the transition from abnormal to normal bipolar switching can be observed through the movement of the new intersection point by increasing the size of the BE. In case of the abnormal bipolar behaviour, the intersection point is directly in the point of origin while in case of the normal bipolar behaviour it has moved to the most negative voltage. Figure y-direction is shown along the BE. Directly below the TE the gradient is strong, but further outwards its value approaches zero. Therefore, increasing the BE does not change the switching behaviour further after the critical size of the BE is reached.The purple curve where the BE is as large as the TE shows abnormal bipolar switching. As expected by symmetry, this curve is identical to the 1D I–V curve with the largest BE .The longer pathways for the oxygen ions are also the reason for the adjustment of the sweeprate compared to the sweeprate in the 1D simulations. In order to obtain normal bipolar switching for the I–V curve with the smallest TE/BE ratio in Fig. I–V curve for a-GaO6. Besides the s-formed shape of the experimental curve which is probably caused by non-linear contact resistances at the electrodes (e.g. Schottky barriers), both experimental and simulated I–V curves match qualitatively very well. Especially the characteristic shape in the first quadrant is reproduced and further investigated. Therefore, the different composition profiles of the oxide at different times within the first quarter of a steady I–V curve are shown in Fig. I–V curve before the maximum of the current density in the first quarter of the cycle (see yellow curve in Fig. The I–V curve does not cross the origin. In a next step, we used a 2D rotational symmetric model to simulate three dimensional devices. The I–V curves with equal sized electrodes showed an abnormal bipolar behaviour identical to the one–dimensional I–V curves. By increasing the size of the bottom electrode while keeping the size of the top electrode constant, we observed a transition from abnormal to normal bipolar switching. First, an intersection point appeared near the point of origin, which then moved with increasing size of the bottom electrode to the most negative voltage, leading to normal bipolar switching behaviour. After a critical size of the bottom electrode is exceeded, no further change is observed. This phenomenon is caused by the gradient of the electrochemical potential of the oxygen ions, which is the driving force for the movement of the oxygen ions. Outside the centre of the device, the gradient is not perpendicular to the electrodes, which results in longer diffusion pathways for the oxygen ions and thus longer transition times for the switching between LRS and HRS. Our model can reproduce clearly the normal bipolar switching behaviour that was found experimentally for a-GaOIn this work, we used a new drift–diffusion model to simulate the bulk switching in binary, highly non-stoichiometric, amorphous oxides with a mobility edge for the electronic conductivity. In a one dimensional parametric study, we tested the influence of several parameters such as the diffusion coefficient of oxygen ions, the maximum voltage, the sweeprate, the sample’s thickness and the initial composition of the oxide. We found that the incorporation of Mott’s concept of a mobility edge is essential. Without the exponential dependence of the electronic conductivity on the oxygen concentration no switching was found. By using a high diffusion coefficient and a small cycle time, we were also able to simulate the experimentally found electromotive force of a polarised cell where the see Fig.  where a Comsol Multiphysics program without any optional modules.For all simulations, we used version 5.3 of the element ratio of 100, while in the remaining interval, there are 100 mesh points with an element ratio of 50 and a symmetric distribution. An exception is the mesh for the 2 V simulations, where we had to use an even finer mesh due to the steep gradients at the electrodes. There, we divided the length into eleven intervals with new intervals beginning after element ratio of 10 and in the remaining interval 50 mesh points with an element ratio of 5 and a symmetric distribution. For both meshes the maximum element size was 2 For the mesh in one dimension, we divided the length into three intervals in order to increase mesh point density at the electrodes. In the one percent next to the electrodes, there are 500 mesh points with Comsol’s element ratio up to 800. The element size was between 1.1For the three-dimensional simulations we used 1000 mesh points at the TE and depending on the size of the BE 1000–10,000 mesh points for the BE with an For all simulations, we used a timestepping between 0.01 and 0.25 s.divergence with a linear element order. For the partial differential equation for the electrochemical potential of the electrons, we used a lagrange shape function with quadratic order.For the one dimensional simulations, we used the PARDISO solver and for the three-dimensional simulations the MUMPS solver. For all models, we set the shape function for the partial differential equation for the concentration of the oxygen ions to Supplementary Information 1.


In the excitable case, we show the threshold for excitability can be made arbitrarily sensitive.Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints. We describe a direct constructive method of realising finite state input-dependent computations on an arbitrary directed graph. The constructed system has an excitable network attractor whose dynamics we illustrate with a number of examples. The resulting CTRNN has intermittent dynamics: trajectories spend long periods of time close to steady-state, with rapid transitions between states. Depending on parameters, transitions between states can either be  It is natural to try to understand computational properties of neural systems through the paradigm of network dynamical systems, where a number of dynamically simple units (i.e. with attracting equilibria or periodic orbits) interact to give computation as an emergent property of the system. This is as much the case for biological models of information processing, pattern generation and decision making as it is for artificial neural networks inspired by these models. A variety of specific models have been developed to describe the dynamics and training of recurrent networks comprised of coupled neurons in biological and artificial settings. The particular challenge that we address here is the construction of arbitrarily complex, but specified, dynamical structures that enable discrete (finite-state) computation in an input-driven system that is nonetheless continuous in both state and time. Clearly, invariant objects of the autonomous system  only form part of the picture and an input-dependent (non-autonomous) approach such as Manjunath et al.  is needeTo help understand the response of systems to inputs the authors introduced in Ashwin and Postlethwaite  a notioncontinuous time recurrent neural network (CTRNN) (Beer Network attractors joining stable equilibria (Ashwin and Postlethwaite NN) Beer . A CTRNNNN) Beer . They caNN) Beer . They arNN) Beer  and (in NN) Beer ) as modeNN) Beer  considerNN) Beer  discusseNN) Beer .CTRNNs are often referred to as “universal dynamical approximators” , using a CTRNN with N cells. The CTRNN we consider in this paper   3) have realises: definition given below) an excitable network attractor, as defined in Ashwin and Postlethwaite  than the one presented here.In terms of the adjacency matrix, for G has vertices, which correspond to (stable) equilibria in the phase space of the dynamical system (excitable connections (sometimes abbreviated to connections) between the equilibria, which correspond to the edges of the graph. When a trajectory in the phase space moves between neighbourhoods of equilibria along a path close to one of these connections, we say that a transition between the equilibria has occurred. We refer to each of the components of the dynamical system  on the values of the four entries in the adjacency matrix k as AT (Active–Trailing) and cell l as LA (Leading–Active). Note that the lack of two cycles means that the cases with Type DD: Type TD: Type LD: Type TL: Type DT: Type DL: The right panel in Fig. From equilibrium entclass1pt{minimaentclass1pt{minimaTo prove the existence of an excitable connection giving a realisation, we consider a perturbation from G in Theorem almost complete in the sense analogous to the similar notion for heteroclinic networks . The inmentclass2pt{minimk there will be a stable equilibrium excitable connection from If parameters are chosen as in Theorem bottleneck regionspontaneous transition past ghost of a saddle-node bifurcation in Strogatz  If alli, j in , some sWhen there is a choice of two out-going connections, one of which is excitable and the other of which is spontaneous, the one chosen by the trajectory will depend on noise amplitudes and other effects: we expect there to be a rich complicated local and indeed global dynamical behaviour, the analysis of which is beyond the scope of this paper.For our first example, we consider the connected graph with two vertices and a single edge joining them, that is g has local extrema at The two-dimensional system of equations is:If n system  when19\dA and B  is modified by the presence of the additional parameter ystem of  with \doFor the specific system , with \dIn Fig. In the above simulations, we have used We extend these results to show the behaviour as both parameters These changes in qualitative dynamics can be explained in terms of the three-dimensional subsystem with quations . In thisT in Fig. as well as further unstable/saddle equilibria. Recall that these equilibria are not on the boundaries of the box (which are not part of the domain). In Fig. In this section, we demonstrate the method of construction described in Sect. U. For the noisy systems, the entries of U. The remaining parameters were set at the default parameter values given in . For example, recent work (Ceni et al.