ASTRA calculated values of power coupled to the ion species, at the dithering H-mode transition, exhibit a similar nonlinear dependence on density. This analysis points to the important contribution of the ion thermal channel to the L-H phase transition. The low-frequency plasma density and D-alpha dithers appear to be accompanied by sudden bursts of magnetohydrodynamic (MHD) activity. A simple model is tested to demonstrate a possible scenario of self-regulation among turbulence, zonal flows, pressure (density) gradient and MHD activities.The dithering H-mode phase, characterized by oscillations, is generally observed at input power values close to the L-H transition power threshold and low plasma collisionalities (low electron density and/or high plasma temperature). Measurements to characterize the dithering phase are presented for the low aspect ratio, high magnetic field tokamak, ST40. The dithering phase oscillation frequency is observed between 400 and 800 Hz and demonstrates an inverse relationship with core plasma density. Dithering phase H-modes are documented across a nonlinear, low-density power threshold operational space, with signature low- and high-density branches. The minimum power threshold for dithering H-mode access is measured at a core, line average electron density of 4.7(±0.5) × 10This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'. Various tokamaks have documented a dithering phase following the initial transition from L-mode, in which there is a sequence of L-H-L transitions or transitional edge localized modes (ELMs) at values of heating power close to Pth [et al. [The transition from a low confinement mode (L-mode) to a high confinement phase (H-mode) has been documented in tokamak plasmas since 1982 [e to Pth –7. UnderP, which eventually becomes dominant and suppresses the plasma turbulence. This hypothesis is consistent with experimental observations of a modulation of the edge rE profile and turbulence level in typical limit cycle oscillations, also frequently named as an intermediate phase, I-phase or dithering H-mode phase on a range of different tokamaks [et al. [Fundamental to the creation of plasma transport barriers and the transition to improved plasma confinement phases is the reduction of electrostatic turbulence by sheared flow. Both larger scale, mean E x B flows  and fine-scale zonal flows  are thought to play active, but different roles in turbulence suppression. Zonal flow models, such as Kim & Diamond's  predatortokamaks ,11,12. I [et al. , who speen, min [en,min have been reported to cover a wide range in different-sized conventional tokamaks in [19 m−3 and 1.5 × 1020 m−3. The larger tokamaks such as JET and JT60-U populate the lower en, min range, medium size tokamaks DIII-D and ASDEX-U lie somewhat higher and the highest values have been measured for the high-field, compact machine, Alcator C-Mod [en,min for spherical tokamaks in the literature.The density dependence of the L-H power threshold has been known for a long time to be non-monotonic on conventional tokamaks, with a minimum power threshold at a given density, ne, min ,15. The amaks in , betweenor C-Mod . The autIt is also important to note that the fundamental dynamics of the H-L transition may also be quite different from that of the L-H, as the plasma conditions that precede the phase change, such as plasma profiles and turbulence are significantly different in the H-mode phase. There have been relatively few H-L transition and power hysteresis studies ,14,17, eIn this paper, the experimental conditions and analysis methods used to study the access to the dithering phase H-mode in the low-density region on ST40 are described in §2. Section 3 describes the experimental characteristics observed for the dithering H-mode phase of the plasmas. The power threshold and temperature analysis are included in §4, along with the power balance calculations for the different plasma species and an extended zonal flow model. The last section comprises a summary of the main results from the study along with planned futurework.. 2a, with plasma major radius, R = 0.46–0.48 m, and minor radius, a = 0.26 m. A representative magnetic configuration at the start of the H-mode, is shown in figure 1b for shot number 9780, at t = 79.7 ms prior to the L-H transition. The general plasma parameters for two shots, #9780, which transitioned to a dithering H-mode, and #9784, which remained in L-mode, are compared in The dithering H-mode phase results presented in this paper are from the compact, high-field, spherical tokamak, ST40  shown infigure 1c for the shots #9780 and #9784.Neutral beam injection (NBI) was the only auxiliary heating method used; one of the injectors provided a series of 0.1–0.2 MW incremental power steps over 11–12 ms. All shots included in this study were fuelled with the deuterium NBI in the quasi-stationary plasma current phase and example NBI power time traces are shown in figure 2a. A plasma density scan was performed for the series of shots in this study at pI/tB = 0.52 MA/2.0 T over a range of, κ = 1.34–1.44, at the L-H transition.The plasma current typically increased from 0.52 MA to a maximum of 0.56 MA over the window of NBI injection, as shown for the example plasmas figure 2e and f. This instrument views along a radial line-of-sight through the mid-plane. The e and f are averaged values over the emission region of He- and Li-like ions and therefore a lowest estimate of the central plasma temperatures. The last L-mode and H-mode In the core plasma, electron and ion temperatures, und 4 nm  with a td. The plasma-stored energy, pW, is evaluated from the reconstructed EFIT [The line averaged core plasma electron density, ted EFIT  magnetohted EFIT .. 3αD emission and αD intensity and rise in The L-H transition for these plasmas is characterized by a transition from L-mode to a dithering H-mode phase. The ng phase ,22,23. TpI, tB and core plasma L-mode t = 61.6 ms for 8 ms. The short reduction in power was sufficient to prevent the plasma from transitioning to the H-mode and provides a very useful L-mode reference shot under very similar vessel and plasma conditions. The L-H transition for shot #9780 occurs at t = 79.8 ms, at which time a difference in plasma energy of ΔpW = 7.3 kJ, pW = 9.9 kJ and b,d, displaying the enhanced energy and particle confinement characteristic of H-mode development. From figure 2f, the corresponding maximum difference in The temporal evolution of two shots with comparable a, in which the average number of cycles over the dithering time window has been considered. The cycle frequency is observed to vary between 400 and 800 Hz over the pW = 35–39.5 MJ and βN = 1.9–2.1 at the L-H transition, compared with peak values in dithering H-mode of pW = 35–45.6 MJ and βN = 1.9–2.54. The data presented in figure 3b clearly show the L- and H-mode segments of the shots to be differentiated by the associated values of stored pW and Nβ.The frequency of the H-mode cycles of the dithering phase are found to decrease with core density, as shown in figure 3. 4LP, is defined at:PIN is the sum of the input power, which in these plasmas are ohmic and NBI, and dpW/dt is the rate of change of stored plasma energy. The value of Pth, have been taken as the values of LP, at the time of the forward and back transitions, defined as the first and final transition into and from the dithering phase, as described above.Following conventional analysis of experimental values in the field, the loss power, Pth for seven plasmas  are plotted in figure 4a as a function of Pth data. These results demonstrate a nonlinear dependence of Pth on Pth from the fit to the data lies in the region of core The values of the L-H and H-L a indicates the predicted value of et al. [19 m−3, where pI in in MA, tB is in T, a and R, are in m. Ryter et al. [eT, iT thermal fluxes, even in the relatively cooler edge plasma region.The vertical shaded area in figure 4r et al.  for a mur et al.  suggest pI and tB accessible in ST40, along with the hot-ion mode plasma intrinsic separation of the ion and electron heating channels.The experimental value of NBI_iP, and electron, NBI_eP, plasma species have been analysed using a time-dependent power balance calculation with the ASTRA code [NBI_iP and NBI_eP are compared with the values of Pth in figure 4a. The behaviour of NBI_iP exhibits a similar trend to Pth, varying nonlinearly with NBI_eP decrease linearly with increasing Pth dependence on The heating power coupled to the ion, TRA code ,25 in MWb. The values of line averaged ion temperature measured using the He-like argon emission, Pth curve.The corresponding values of core Pth, also plotted in figure 4a. These H-L transitions appear to be triggered by the elevated values of dithering phase H-mode plasma density at the limited input power. The H-L Pth is measured to be up to 10% lower than the corresponding L-H Pth. For the observed H-L transitions, the values of b are observed to be comparable with the forward transition values, for the lower plasma density, iT is measured to be 1.2 times higher than for the L-H transition. The transition from H-mode to L-mode is less well controlled and therefore more difficult to access than the forward transition. While this limited dataset of two points indicates a small amount of hysteresis in power and differences in ion temperature observations over the density scan, more data are required over the The H-L transition for two of the plasmas (#9781 and #9831) occurred within the NBI heating phase and were used to determine the H-L a), dpB/dt (b) and D-alpha (c) for shot #9780. The dominant frequency of the MHD activity can be seen f < 1 kHz. The observed abrupt occurrences of large fluctuations in dpB/dt are associated with a sudden rise in D-alpha and a sudden collapse of The physical origin of the observed dithering is not entirely clear given no experimental measurements of edge plasma turbulence, rotation, radial electric field, etc. Although the dithering cycles may be due to self-regulation between self-generated zonal flows and turbulence , it seemet al. [V are generated by turbulence through the first term αEV on the right-hand side of equation (a3) while damped directly by mE as well as collisional damping. The example time evolutions of the mean ion pressure gradient, p , MHD activity, mE, and turbulence amplitude, E, together with input power, P, are shown in P is taken to increase up to P = 0.075 at = 2500 and then ramped twice down to P = 0.015 at t = 2600, as shown in figure 6a. Model parameters (see appendix A) are chosen to ensure the appearance of dithering shortly after the L-H transition.Assuming electrostatic turbulence in the L-mode, including MHD pressure gradient-driven instabilities in  would leet al. . As notea,b shows that as turbulence amplitude E grows, zonal flows V are amplified starting around t ≈ 1800, marking the L-H transition at crP ≈ 0.7. However, when V grows to a sufficiently large amplitude, it damps E, causing a certain phase shift between the oscillations of E and V. That is, V and E do not share a similar phase. At the same time, turbulence regulation by V leads to steeping of the edge pressure gradient p, causing MHD activity mE in figure 6f, which damps not only p but also V (through the damping term m VE in equation (a3)). MHD activity is also manifested as a sudden spike in c and powerloss d. The maximum power at P = 0.075 at t = 2500 is about 7% above crP ≈ 0.7. Self-regulation among E, V, mE and p (mean shear flow ∝ p2) can be seen more clearly in zoomed-in views in figure 6e,f. Note that because of the damping of V by magnetic activity, the self-regulation between turbulence E and zonal flows V is less evident than what was observed in [mE = 0 were used for the parameter values used in Figure 6erved in . If Em =. 5Pth for access to a dithering H-mode phase. All the plasmas remain in the dithering H-mode phase before transition back to L-mode due to the available power margin remaining close to the L-H Pth and in the absence of plasma density feedback control.A plasma density scan has been performed on the ST40 that shows a minimum Pth is measured has been observed at pI and tB in governing the Pth on ne in the nonlinear, low-density region. The calculated values of NBI_iP show a similar nonlinear dependence on core NBI_eP is observed to have a weak negative linear dependence over the density range scanned. These results indicate the ion thermal channel plays a key role in accessing the H-mode.The core electron density at which the minimum The line averaged core ion temperature just prior to the L-H transition has a peak value of Data for the power threshold for H-L transition have been included for two plasmas in this study and indicate a maximum of 10% hysteresis in the power threshold. Experiments are planned in forthcoming campaigns to carefully study and evaluate hysteresis in the ST40 H-mode.An extended self-regulatory limit cycle model has been developed to include turbulence amplitude, zonal flows, pressure gradient and MHD activity. This model reproduces the qualitative features of the dithering H-mode cycles well and points to the possible contribution of low-frequency MHD, due to a steep density or pressure profile, to the L-H-L cycle in the dithering phase of the plasmas.It will be interesting to include the effect of additional terms in forthcoming experimental H-mode and L-H/H-L transition investigations and power balance calculations; factors such as NBI shine through losses, fast ion losses due to charge exchange and ion orbit processes and radiated power. In addition, experiments to study the role of the edge, pedestal and SOL plasma parameters are foreseen on ST40 with an upgraded set of Charge Exchange Recombination Spectroscopy and Thomson Scattering diagnostics. Dedicated experiments are also planned with the updgraded diagnostic suite to build and expand the H-mode and L-H/H-L transition database with different plasma configurations.


For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most Directed Additive Spanner asks whether G has an additive t-spanner with at most Directed Multiplicative Spanner admits a polynomial kernel of size Directed Multiplicative Spanner can be solved in Directed Additive Spanner is k for every fixed t and k.We initiate the parameterized complexity study of minimum  G, a spanner is a spanning subgraph of G that approximately preserves distances between the vertices of G. Graph spanners were formally introduced by Peleg and Schäffer in  to denote the subgraph of G induced by X. For a set of vertices S, S, that is, v, we write S , S . A subgraph H of a (directed) graph G is a spanning subgraph of G if G has a topological ordering of its vertex set, that is there exists path with the vertices end-vertices of P and we say that P is a -path. A single vertex path is trivial, and for a trivial P is a -path. All considered paths are assumed to be simple, that is, length of a path is the number of edges  in the path. Also A(P) denotes the arc set of the path P. For a -path v, w)-path concatenation of distance between u and v in G, that is, the length of a shortest -path; we assume that u, v)-path in G. Clearly, We write t be a positive integer. It is said that a spanning subgraph H of G is a multiplicative t-spanner if H of G is called an additive t-spanner if Let G be an arc wighted directed graph, that is, we a given a weight (or length) function length of an arc e. The length of a weighted path weighted distanceG, it is said that a spanning subgraph H a weighted multiplicative t-spanner if t is not required to be an integer.We also consider the weighted variant of spanners for directed graph. Let Directed Multiplicative Spanner. We show that the problem admits a polynomial kernel and then complement this result by obtaining an Directed Multiplicative Spanner is Weighted Directed Multiplicative Spanner is k only. These results are based on locality of multiplicative spanners in the sense of the following observation made by Peleg and Schäffer [In this section, we consider Schäffer .t be a positive integer (or H of a directed graph G is a (weighted) multiplicative t-spanner if and only if for every arc u, v)-path in H of length at most t  in the weighted case).. Let t t be a positive integer  and let G be a directed graph. For an arc G, we say that a -path P is a t-detour for a if the length of P is at most t (t times the length of a in the weighted case) and P does not contain a. By Observation Directed Multiplicative Spanner for , it is necessary and sufficient to identify k arcs that have t-detours that do not contain selected arcs. Then H can be constructed by deleting these arcs. Notice that this observation holds for both unweighted and weighted spanners. However, for the weighted case, the number of arcs in a t-detour may be arbitrary and depends on the length of a.Let mentclass2pt{minimDirected Multiplicative Spanner admits a polynomial kernel.In this subsection, we show that Directed Multiplicative Spanner has a kernel of size G, t, k) be an instance of Directed Multiplicative Spanner. Clearly, if G, t, k) is a yes-instance, and our algorithm returns a trivial yes-instance in this case. We assume from now that Let  is a yes-instance of Directed Multiplicative Spanner.We say that obayashi  for consG, t, k) is a yes-instance of Directed Multiplicative Spanner.If t-detour for a.Let select an arbitrary set set We show by induction, that the sets Let mentclass2pt{minimNow we select arcs t-detours t-spanner. Therefore,  is a yes-instance of Directed Multiplicative Spanner. Let mentclass2pt{minimBy Claim Directed Multiplicative Spanner and stop.If From now, we assume that t-detours for S contrary to the undirected case, where all the edges of t-detours are in cycles of length at most t-detours themselves. We use the following procedure to mark the crucial arcs of potential detours.The analog of Reduction Rule Marking Procedure Let (i)u, v)-path P in P is at most t, then mark the arcs of P.For every (ii)t, then mark the arcs of find a shortest t, then mark the arcs of find a shortest t, then mark the arcs of find a shortest For every ordered pair of two distinct arcs Observe that marking can be done in polynomial time by Dijkstra’s algorithm. Denote by L the set of marked arcs. Our final rule constructs the output instance.H, and for the obtained Consider the graph We argue that the rule is safe.G, t, k) is a yes-instance of Directed Multiplicative Spanner if and only if  is a yes-instance of Directed Multiplicative Spanner. Then, by Observation k distinct arcs t-detours Suppose that -path in t-detour t-detour for Suppose that S. Let u). Note that S are vertices of u, v)-walk u, v)-walk of length at most t in t-detour Assume that t-detour Directed Multiplicative Spanner.We obtain that for every mentclass2pt{minimDirected Multiplicative Spanner. By Observation k distinct arcs t-detours G, t-detours in G. By Observation G, t, k) is a yes-instance. For the opposite direction, assume that mentclass2pt{minimmentclass2pt{minimt arcs for each S|t arcs are marked in this step. In step (ii), we mark at most 3t arcs for each ordered pair of arcs of S. Hence, at most To upper bound the size of Since each of the reduction rules and Marking Procedure can be applied in polynomial time, we conclude that the total running time of our kernelization algorithm is polynomial. k arcs of G and verifies whether the deletion of these arcs gives a multiplicative t-spanner, we obtain the straightforward Directed Multiplicative Spanner. If we use the intermediate steps of the kernelization algorithm, then the running time may be improved (upto some constants in the exponent) to S of t-good arcs and execute Reduction Rule S has size at most k, we check whether t-spanner by computing the distances between every pair of vertices. However, we can slightly improve the parameter dependence by making use of the random separation technique proposed by Cai, Chan, and Chan in [Directed Multiplicative Spanner.Combining Theorem mentclass2pt{minim Chan in   be an instance of Directed Multiplicative Spanner. If G, t, k) is a yes-instance, and if G, t, k) is a no-instance. From now we assume that Let  is a yes-instance of Directed Multiplicative Spanner for  if and only if there are k arcs that have t-detours avoiding these arcs. We use random separation to distinguish the arcs that have t-detours and the arcs of the detours. We randomly color the arcs of G by two colors red and blue. An arc is colored red with probability k red arcs that have t-detours composed by blue arcs. Let R be the set of arcs colored red and let B the set of blue arcs. For u, v) has a t-detour with blue arcs by finding the distance between u and v in S of all red arcs with blue t-detours. If G, t, k) is a yes-instance by Observation By Observation mentclass2pt{minimG, t, k) is a yes-instance of Directed Multiplicative Spanner. Then by Observation k distinct arcs t-detours L are colored blue is at least t-detours are blue is at least t-detours blue is at most G, t, k) is a no-instance with the mistake probability at most Suppose that  be an instance of Independent Set and let G and denote For every construct a vertex construct for every For every Denote the obtained directed graph by D  is a yes-instance of Independent Set if and only if Directed Multiplicative Spanner.We claim that  be an instance of Independent Set and let Weighted Directed Multiplicative Spanner as follows. First, we construct D for G, k) is a yes-instance of Independent Set if and only if Weighted Directed Multiplicative Spanner. For the second claim, we modify the above reduction. Let ..IndependG, k) be an instance of Independent Set and let t be a positive integer. Denote by G.For every if if For every Denote the obtained directed graph by D  is a yes-instance of Independent Set if and only if  is a yes-instance of Directed Additive Spanner.Let -path in D contains at most one arc of S. The proof is by contradiction. Assume that there are u, w)-path P such that P contains at least two arcs of S. Let P. Since the arcs of S correspond to vertices of the independent set I, G. Therefore, D contains the P is a shortest path containing P should have length at most We first claim that for every two vertices u and w be two vertices of D. Let P be a shortest -path in D. If P is a path in P is not a path in P contains a unique arc P and let P plus the length of t-spanner of D.Now let D, t, k) is a yes-instance of Directed Additive Spanner. Then there is a set of k arcs t-spanner. Observe that if D has an -path P that does not use the arc . Otherwise, G. Assume, for the sake of contradiction, that this is not the case and there are G. Let D. Since t-spanner. We conclude that I is an independent set of G and, therefore,  is a yes-instance of Independent Set. Now we assume that (Directed Multiplicative Spanner admits a kernel of size (Weighted) Directed Multiplicative Spanner is Multiplicative Spanner is FPT on general graphs when parameterized by k only for both undirected and directed cases. Also, is the weighted version of Multiplicative Spannerk and t on general graphs? Again, this question is open for both undirected and directed graphs.We proved that Directed Additive Spanner is Directed Additive Spanner is tractable on some special classes of directed graphs, like planar directed graphs. We believe that this problem may be interesting even if the distortion parameter t is assumed to be a constant.Further we proved that H of a directed graph G is a multiplicative t-roundtrip-spanner if for every two vertices u and v, H approximates the sum of the distances between any two vertices in both directions. Is the analog of Directed Multiplicative Spanner for roundtrip spanners G constructed as follows: construct two vertices u and v and an arc , and then add a -path v, u)-path G. However, H has no short detour for . It is also possible to define additive t-roundtrip-spanners and consider the analog of Directed Additive Spanner. We conjecture that this problem is at least as hard as Directed Additive Spanner.Another possible direction of research is considering different types of directed graph spanners. For example, what can be said about the roundtrips spanners introduced by Roditty, Thorup, and Zwick ? A spannmentclass2pt{minim


Background: Low-rank approximation is used to interpret the features of a correlation matrix using visualization tools; however, a low-rank approximation may result in an estimation that is far from zero, even if the corresponding original value is zero. In such a case, the results lead to a misinterpretation. Methods: To overcome this, we propose a novel approach to estimate a sparse low-rank correlation matrix based on threshold values. We introduce a new cross-validation function to tune the corresponding threshold values. To calculate the value of a function, the MM algorithm is used to estimate the sparse low-rank correlation matrix, and a grid search was performed to select the threshold values. Results: Through numerical simulation, we found that the false positive rate (FPR), interpretability, and average relative error of the proposed method were superior to those of the tandem approach. For the application of microarray gene expression, the FPRs of the proposed approach with  It is essential in applications to compute the correlation matrix and present it with a heatmap  to underA low-rank approximation address problem (a) . VariousWhile the low-rank correlation matrix has the above advantages, (i) the number of correlation coefficients to be interpreted becomes problematic when the number of variables is large, making interpretation difficult, and (ii) according to the Eckart–Young–Mirsky theorem , the errTo overcome this, in this study, we proposed a new approach to estimate sparse low-rank correlation matrices. The proposed approach, combined with a heatmap, provides a visual interpretation of the relationships between the variables. There are two types of techniques available for the sparse methods of the correlation matrix and the covariance matrix ,10. The The proposed approach adopts an approach that uses hard thresholding based ,24 thereThe summary of the proposed method is as follows: for small sample sizes and noisy data, a sparse low-rank correlation matrix can be used to emphasize the correlation coefficients between related variables. In addition, the inclusion of sparse constraints eliminates the problem of misunderstanding and facilitates interpretation. Furthermore, the direct estimation of the correlation matrix instead of the covariance matrix reduces the computation time comparatively. We introduce a new cross-validation function to estimate sparse low-rank correlation matrices modifying those used in Refs. ,24. ThisThe rest of this paper is structured as follows. We explain the model and algorithm in In this section, we present the proposed approach for estimating a sparse low-rank correlation matrix. First, an estimation of a low-rank correlation matrix is described based on the MM algorithm ,4. Next,p is the number of variables. Here, d, ⊙ is the Hadamard product, Let rij)rij∈−,1=f=iwijrijyj≤−yi(t−1)quation (fi(yi|{yjiwijrijyj≤−yi(t−1)Algorithm 1 Algorithm for estimating the low-rank correlation matrixInput:Output:Initialisation: Set j and set   whiledo 1: forp 2:   3:    Calculate  4:    Calculate  5:    Update Equation .End for 6:   7:  End while 8: returnj 9: Using the Lagrange multiplier method and Equation , the updWe adopt hard thresholding to estimate the sparse low-rank correlation matrix in the proposed approach. To determine threshold values, we introduce a cross-validation function based on Ref. . The purLet  science . Let Wh(fined asTh(α)(R)=p)wherer˜ij=rij·d, and the correlation matrix d, such as minimizing k represent the index of the number of iterations for cross-validation, and d, K times and the proposed cross-validation function is calculated as follows.K is the number of iterations for the cross-validation. Among the candidates for threshold values, Algorithm 2 Algorithm of Cross-validation for tuning proportional thresholdsInput: candidates of threshold values Output:Initialisation: Set   Forto  1: ForK  2:    3:   Split   4:   Calculate both   5:   Calculate Algorithm 1 is applied to estimate   6:   Given End For  7:    8:  calculate   9:  End For10: 11: return12: To estimate a sparse low-rank correlation matrix, we introduce the modified proportional threshold operator based on Equation  because follows;Th(α),d. Then2, Ref.  determinfollows.CV(h(α),dFinally, Equation  among thEquation .This section presents a numerical simulation to evaluate the proposed approach. The numerical simulation was conducted based on Ref. , with soIn this subsection, the simulation design is presented. The framework of the numerical simulation consists of three steps. First, artificial data with a true correlation matrix are generated. Second, sparse low-rank correlation matrices are estimated using two methods, including the proposed method. In addition, a sample correlation matrix and sparse correlation matrix based on the threshold also apply. Third, using several evaluation indices, these estimated correlation matrices are evaluated and their performances are compared.I and J be a set of indices for the rows and columns of the correlation matrices, respectively. In addition, p. In this simulation, we set d, the result of the estimation In this simulation, three kinds of correlation models are used. Let e set asrij(1)=1−,2,⋯,p),rij(2)=0.⋯,p)and,rij(3)=0.e set asrij(1)=1−,2,⋯,p),rij(2)=0.al lasso ) = 18 paNext, the settings of the numerical simulation are presented. For the summary, see CVglasso package is used [R. The correlation matrix is then calculated from the estimated sparse inverse covariance matrix.Finally, in setting four, we selected five methods: the proposed approach, tandem approach, sample correlation matrix calculation, and the sparse correlation matrix estimation based on threshold value  with modst step. 1K∑k=1K∥W in Ref. . In the  on Ref. . In shorEquation  is used  in Ref. ). The se in Ref. . To sele is used  in R. ThLikewise, as in the approach pursued in Ref. , we adopEquation , EquatioEquation , and EquEquation , respectg index. Sparsity=g index. Sparsity=Here, we present the results of applying both the proposed approach and the tandem approach to the microarray gene expression dataset in Ref. . This reIn Ref. , the samG indicates the number of classes, such as NB, RMS, BL, and EWS, g, g for gene j, j, and g for gene j. Here, if j is considered as “informative” because the corresponding j tends to include information such that each class is discriminated. From the calculated Next, to construct the “informative” class and the “non-informative” class, the F statistics are calculated for each gene, as follows:To compare the results of the proposed approach with those of the tandem approach, the FPR is calculated. For the tandem approach, see g index: withinclaThis section presents the results of the numerical simulation and real application.In this subsection, we present the simulation results by the true correlation models. For the relative error of the For the estimated correlation matrices, In this subsection, the results of the application of the microarray gene expression dataset are shown. For the estimated original correlation matrix, Jiang (2013) with modifications, the proposed approach tandem approach, and graphical lasso, see Next, This study proposed a novel estimation method for sparse low-rank correlations based on the MM algorithm. The approach overcomes the problem of estimating low-rank correlation matrices. The low-rank approximation is an a potent tool, and the approach provides us with a straightforward interpretation of the features because the contrast of the estimated coefficients becomes larger. However, these estimates sometimes lead to misinterpretations. Even if the true correlation coefficient is zero, the corresponding estimated coefficient of the low-rank approximation without sparse estimation may be greater than zero. To confirm the efficiency of the proposed method, we performed numerical simulations and experimented using a real example, which involved the use of a microarray gene expression dataset. In the case of the real example, the FPR of the proposed approach with Next, we refer to each method compared. The sample correlation matrix was used as a reference and for comparison. For Jiang (2013), concerning modifications, the numerical simulation results confirm that the F-norm and the S-norm are better than the proposed approach and the tandem approach because the low-rank approximation is not performed. Furthermore, Jiang (2013) with modifications is better than the sample correlation matrix without sparse constraints. Graphical lasso is a method for the sparse estimation of the inverse of the covariance, and the computed correlation matrix is not necessarily a sparse. Therefore, FPR, sparsity, and within-class sparsity were not good compared to the other methods through numerical simulations and examples of real-data applications. In other words, when a correlation matrix is estimated, it would be better to estimate a direct correlation matrix or a covariance matrix. The TPR, FPR, and sparsity of the tandem approach are almost identical to Jiang (2013) with modifications. The tandem method has a higher FPR than the proposed method and worse results for sparsity and within-class sparsity, which are indicators of interpretability. Furthermore, the proposed method performed better for the F-norm and the S-norm because the tandem method does not take threshold values into account. However, the numerical simulation results show that the TPR tends to be better than the proposed method.Here, we show the recommendations of the proposed approach. First, the proposed approach can provide the interpretable sparse low-rank correlation matrix from the result of both the sparsity of the numerical simulation and the within-class sparsity of the real example. Second, in a real example, the sparse low-rank correlation matrix estimated by the proposed approach was close to previous studies . HoweverAlthough the proposed approach showed promising results in both experiments, several limitations need further investigation. First, when the rank is set low, the TPRs of the proposed method were low compared to those of the tandem approach. The relationship between the determination of the rank and the corresponding TPR, F-norm, S-norm, sparsity, and within-class sparsity was a trade-off. Therefore, a method for a more effective determination of the rank should be developed. As one of the solutions to the problem, we can consider the introduction of a nuclear-norm regularization . Second,


Deep neural networks have been successfully applied to generate predictive patterns from medical and diagnostic data. This paper presents an approach for assessing persons with Alzheimer’s disease (AD) mild cognitive impairment (MCI), compared with normal control (NC) persons, using the zoom-in neural network (ZNN) deep-learning algorithm. ZNN stacks a set of zoom-in learning units (ZLUs) in a feedforward hierarchy without backpropagation. The resting-state fMRI (rs-fMRI) dataset for AD assessments was obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). The Automated Anatomical Labeling (AAL-90) atlas, which provides 90 neuroanatomical functional regions, was used to assess and detect the implicated regions in the course of AD. The features of the ZNN are extracted from the 140-time series rs-fMRI voxel values in a region of the brain. ZNN yields the three classification accuracies of AD versus MCI and NC, NC versus AD and MCI, and MCI versus AD and NC of 97.7%, 84.8%, and 72.7%, respectively, with the seven discriminative regions of interest (ROIs) in the AAL-90. Neuroscience has provided inspiration for and insight into artificial neural networks, including deep-learning networks. However, the field of artificial neural networks has been optimized through mathematics rather than neuroscientific findings . In addiDeep-learning algorithms with a hierarchical architecture are exploited as representative learning schemes, including restricted Boltzmann machines (RBMs), using local unsupervised pretraining layers from the bottom to top layers ,6,7. A dA simple feedback alignment mechanism that adjusts weights by multiplying errors with even random synaptic weights performs as effectively as backprop . The algAs one of the features of deep-learning algorithms used in unsupervised learning, the pretraining is determined by starting with random weights. Biological learning is more advantageous for the optimization of weight initialization due to large numbers of trials and errors. However, because backprop consumes considerable time to correct the weights after initialization, optimization using various weight initializations is difficult to achieve.An intuitive way to consider diverse brain learning paradigms is to find another sup-pattern that is different from the main pattern. For example, ambiguous forms for a particular pattern can be learned through a more detailed look using a magnifying glass. This allows us to make more accurate judgments by learning the causes from a misjudgment, prejudice, or misclassification. In other words, learning can come from mistakes that are to be discarded or ignored. At the same time, it is possible to learn more precisely only through the refined instances. This paradigm reinforces learning efficiency through rewards, from both mistakes and well-learned domains simultaneously.According to Wikipedia, the dictionary meaning of metacognition is an awareness of one’s thought processes and an understanding of the patterns behind them. When metacognition is applied to a person, it means that the person understands his or her learning process or judgment process or thinking process. This concept was applied to the learning algorithm in this paper. We propose a feedforward zoom-in neural network (ZNN) deep-learning algorithm that implements a learning paradigm called metacognitive learning. A ZNN stacks layers, each of which consists of a set of zoom-in learning units (ZLUs) in a feedforward manner. In a ZLU, meta-cognitive information is accumulated through subpattern learning and fine-tuning learning according to the learning results after learning occurs. Through subpattern learning, another pattern is found as meta-cognitive information from errors in standard learning. Through fine-tuning learning, a more detailed pattern for standard learning is found as meta-cognitive information.The outputs of the ZLUs in a layer are forwarded to a higher layer to achieve a gradual improvement in the discrimination power. This brings about a dimensionality reduction with structural flexibility by decreasing the number of ZLUs as the learning of the ZNN moves to higher-level layers .In this paper, a deep-learning model based on a neural network with weighted fuzzy membership functions (NEWFMs)  is propoThe proposed ZNN is a supervised feedforward deep-learning system using ZLUs implemented by the NEWFMs. The structure of the ZNN, illustrated in The basic processes of the ZNN are executed by the neuronal ZLU module. Each ZLU generates two subpatterns and a refined defuzzified output for the next layer. The subpatterns and the refined defuzzified output include metacognitive information.A ZLU consists of two-part learning, as shown in The first advantage of a ZLU module is that the load of learning can be distributed to the ZLUs according to the divided input features. Second, a ZLU module can be assembled flexibly to find a pattern of functional connectivity of neural networks. As the third advantage, the cost function for each ZLU module could first be applied locally, which may follow the cognitive processes of the human brain learning inferences of a hierarchical principle by fusing or filtering out of the local decisions .As the main contribution of ZLU, it applies a zoom-in learning process. A neuroscience basis for the learning scheme in the human brain is provided by the metacognitive learning method that monitors uncertainty regarding a decision ,20, as iZLU is a basic unit module of the ZNN algorithm. Each ZLU module generates two types of subpatterns and refined outputs for the next ZLU layer. The layerwise supervised learnings in ZNN are executed to improve the learning ability by zooming in on the input patterns using the ZLUs. Feedforward learning of a ZNN without backpropagation in deep-learning algorithms provides an efficient learning method by eliminating the vanishing gradient problem.The ZNN algorithm is divided into training and testing parts, i.e., a training algorithm and test algorithm of the ZNN, respectively. Algorithms 1 and algorithm 2 show train and test algorithms. To describe the training and testing that takes place in a ZLU, once the standard training, instance grouping, and zoom-in training are completed in a ZLU, as indicated by the solid lines in Train Algorithm of ZNNAlgorithm 1: Input Layer 1.1 Split train input data with n features into the k subsets with   n/k features such that {I0,1}, {I0,2}, …, {Ik0,}2 i-th ZLU layer  2.1 Let ZLUi,j be j-th ZLU in i-th ZLU layer 2.2 For each {Ii−1,j}, where j = 1 to k  2.2.1 Assign {Ii−1,j} to ZLUi,j as input 2.3 For eachZLUi,j, where j = 1 to k  2.3.1 Standard training   2.3.1.1 Standard training using NEWFMi,j from {Ii−1,j}   2.3.1.2 Instance grouping: divide {Ii−1,j} instances into      misclassified instances (MI) {Mi,j} and correctly      classified instances (CCI) {Ci,j}  2.3.2 Zoom-in training   2.3.2.1 Subpattern training from {Mi,j} using      NEWFMi,j,M   2.3.2.2 Refine training from {Ci,j} using NEWFMi,j,C  2.3.3 Zoom-in output 2.3.3.1 Output TSD {Ti,j,M} using NEWFMi,j,M from {Ii−1,j} 2.3.3.2 Output TSD {Ti,j,C} using NEWFMi,j,C from {Ii−1,j} 2.4 Split the TSDs {Ti,1,M, Ti,1,C, Ti,2,M, Ti,2,C, …, Ti,n,M, Ti,n,C}   into {Ii,1}, {Ii,2}, …, {i,nI}, where n is the number of ZLUs   in the (i + 1)-th ZLU layer 2.5 i = i + 1, k = n, and go to 2 until predefined i is reached3 Output Layer 3.1 Train by the NEWFMi using {Ii−1,1}, {Ii−1,2}, …, {Ii−1,k}1 Test Algorithm of ZNNAlgorithm 2: Input Layer 1.1 Split test input data with n features into the k subsets with   n/k features such that: {I0,1}, {I0,2}, …, {Ik0,} as in 1.1 ofTrain Algorithm of ZNN   2 i-th ZLU Layer  2.1 For each {Ii−1,j}, where j = 1 to k  2.1.1 Assign {Ii−1,j} to ZLUi,j as input  2.1.2 Zoom-in test:   2.2.2.1 Output TSD {Ti,j,M} using NEWFMi,j,M from {Ii−1,j}   2.2.2.2 Output TSD {Ti,j,C} using NEWFMi,j,C from {Ii−1,j} 2.2 Split the TSDs {Ti,1,M, Ti,1,C, Ti,2,M, Ti,2,C, …, Ti,n,M, Ti,n,C}   into {Ii,1}, {Ii,2}, …, {Ii,n}, where n is the number of ZLUs   in the (i + 1)-th ZLU layer 2.3 i = i + 1, k = n, and go to 2 until the output layer is reached3 Output Layer 3.1 Output TSD {Ti} by the NEWFMi using {Ii−1,1}, {Ii−1,2}, …,   {Ii−1,k}1 In this section, the experimental results for assessing persons with Alzheimer’s disease (AD) and mild cognitive impairment (MCI), compared with normal control (NC) persons, using the proposed ZNN deep-learning algorithm, are presented to evaluate the ZNN algorithm with the discriminative regions of interest in the Anatomical Automatic Labeling (AAL-90) model.The experimental dataset contains the resting-state functional magnetic resonance imaging (rs-fMRI) data concerning 34 AD patients, 89 MCI patients, and 45 NC persons. It was obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database . The rs-To obtain an overall change in each ROI with 2000 to 3000 voxels, the average of voxels (AOV) of each ROI was generated as a representative signal of the ROI. The features were extracted using the Haar wavelet transform (HWT) from the 140-time series of AOVs. In addition, the local and global graph measures  were useThe series of experimental structures led to a 140-time series of ROIs, AOVs, feature extraction, feature selection, region selection, and ZNN classification, as shown in From the 140-time series of AOVi of ROIi a,b, the Finally, the highly accurate ROIs that were candidates for discriminative ROIs for AD assessments were selected for input into the ZNN model e,f. In pAD assessments by the proposed ZNN model have three pairs of classifications: AD versus NC-MCI (A-NM), NC versus AD-MCI (N-AM), and MCI versus AD-NC (M-AN). The ZNN model was run with a hold-out verification method by setting 23 subjects in the dataset as training sets and the rest  as test sets.ZNN yielded the three classification accuracies of A-NM, N-AM, and M-AN as 97.7%, 84.8%, and 72.7%, respectively, as shown in The increases in accuracy with the stacking of ZLU layers are shown in Ref.  shows 96The 16 most prominent ROIs in the AAL-90 were selected in accordance with the accuracies of the ROIs in Some of the ROIs in a column in The most discriminating ROI in http://nitrc.org/projects/bnv accessed on January 2020) was used to create the images of the ROIs.In this paper, we proposed a deep neural network model, ZNN, to classify Alzheimer’s diseases, which is a new feedforward deep-learning model using brain-inspired metacognitive learning. The ZNN, model without a gradient descending problem in backprop, simulates activity-dependent learning using ZLU units, such as the synaptic plasticity in the brain. A neuroscientific basis for the learning scheme of the metacognitive learning in the human brain  is impleIn addition, the ZLU units enhance the connectivity of the neural networks by connecting the block-type neural network units in a flexible manner. In the proposed model, by using 10 graphic features and h\Haar wavelet coefficients together as classification features, we obtained the effect that the regional characteristics of the brain were more clearly reflected in the classification through the Haar wavelet. The proposed model can also be used to evaluate other diseases. The features used in this method are features that can be extracted from images and numerical data. As the data used for the classification of diseases are mostly image or numerical data, it is possible to apply this model.The proposed algorithm yields a 97.7% classification accuracy for AD versus SCI-MCI, 84.8% classification accuracy for SCI versus AD-MCI, and 72.7% classification accuracy for MCI versus AD-SCI, using the discriminative ROI specifications in the AAL-90. Thus, ZNN learns more efficiently through the zoom-in learning processes following a human-like approach in the way it acts. A further matter to be considered is that AD and SCI are classifications in which symptoms are clearly distinguished. However, as MCI is an intermediate state between AD and SCI, the accuracy of the classification of MCI and others is lower than that of AD and SCI. Another document that shows that the MCI classification results are relatively low is .The importance of classification of MCI is gradually increasing. Accurate classification of MCI enables early diagnosis or prevention of dementia. This can slow the progression of dementia, alleviate symptoms, or increase the probability of a cure. Therefore, improving the classification accuracy of MCI is a future research task.One limitation in this study was that the number of data used was not balanced. We need to balance the data with additional up-to-date data from ANDI. Recent data are continuously accumulating on the ANDI site, and it is necessary to experiment with the accumulated data. We have one more limitation: As the datasets collected from ANDI were not all from the same machine , they ma


Nature Communications 10.1038/s41467-022-32162-x, published online 30 July 2022Correction to: The original version of the These errors have been corrected in the PDF and HTML version of the article, and the HTML has been updated to include a corrected version of the Updated Supplementary Information


Although language-family specific traits which do not find direct counterparts outside a given language family are usually ignored in quantitative phylogenetic studies, scholars have made ample use of them in qualitative investigations, revealing their potential for identifying language relationships. An example of such a family specific trait are body-part expressions in Pano languages, which are often lexicalized forms, composed of bound roots  and non-productive derivative morphemes . We use various statistical methods to demonstrate that whereas body-part roots are generally conservative, body-part formatives exhibit diverse chronologies and are often the result of recent and parallel innovations. In line with this, the phylogenetic structure of body-part roots projects the major branches of the family, while formatives are highly non-tree-like. Beyond its contribution to the phylogenetic analysis of Pano languages, this study provides significative insights into the role of grammatical innovations for language classification, the origin of morphological complexity in the Amazon and the phylogenetic signal of specific grammatical traits in language families. It comprises approximately 33–34 (extant and dormant) languages from neighbouring territories in eastern Peru, western Brazil and northern Bolivia. There have been various internal classification proposals for the Pano language family in the literature, but there is no full agreement on the structure of the Pano phylogenetic tree, the classification of some languages, and the number of major branches –5. This figure 1Pano languages exhibit a significant list of shared grammatical features, which may be suggesting a shallow time-depth . Among tmɨkɨn, which is synchronically non-segmentable, but can be diachronically analysed as the combination of the root mɨ- ‘hand’ and the formative -kɨn. The root mɨ- ‘hand’ can also function as a prefix and as such it can be attached to nouns , and verbs (mɨ-táʃka ‘to slap on the hand’ [< táʃka ‘to slap’]). Many expressions related to external body-parts exhibit a similar pattern: Iskonawa tɨhu ‘neck’ (tɨ-hu), Kapanawa hana ‘tongue’ (han-a) and Poyanawa kɨha ‘mouth’ (kɨ-ha). The forms tɨ- ‘neck’, han- ‘tongue’, kɨ- ‘mouth’ are synchronic body-part prefixes in those languages and, thus, they can be combined with further nouns, verbs and adjectives .tɨ-, but we find substantial variability regarding the formatives recruited for the formation of the lexicalized body-part expressions . In some other instances, the root itself exhibits variation across the languages . We also find full lexical innovations, for instance, piti ‘food’ is the word for ‘tooth’ in Chaninawa, Mastanawa, Sharanawa, Yaminawa and Nawa; while tɨtun ‘neck’ in Matis is ‘Adam's apple’ in Shipibo-Konibo. Finally, there are some cases of stable lexicalized forms in which both the root and the formative are shared by all or almost all the languages in our database . At least some of these stable forms might have originated as monomorphemic words (see the discussion in 4.1).Body-part roots and body-part formatives do not exhibit the same history and the same chronology. We often encounter that body-part roots are stable across languages while body-part formatives may exhibit significant cross-linguistic variation. For example, all the terms for ‘neck’ in the Pano languages in our database share the body-part root ma ‘head’, *βu ‘hair’ and *βɨ ‘eyes, forehead’. In addition, there are four formatives combined with them: -ʂo, -pi, -pu and -ʂka. As an illustration of the intricacies of body-part terms for Pano classification, In this paper, we explore the history of body-part expressions in Pano aiming to quantify and understand their diachronic development. We tease apart the phylogenetic behaviour of the roots and the formatives, and we implement data analysis and clustering techniques to measure their stability. We then explore how tree-like these roots and formatives are, and investigate their potentiality for shedding light on the phylogeny of the Pano languages and for contributing to further topics in the linguistic history of Amazonia. Body-part concepts are often claimed to be basic vocabulary and therefore they are expected to be stable and conservative , p. 132.. 2. 2.1https://digling.org/edictor). The conversion procedure required, among others, to standardize phonetic transcriptions by segmenting distinct sounds from each other (by adding spaces) and by using the B(road)IPA transcription system proposed by the Cross-Linguistic Transcription Systems reference catalogue ([https://clts.clld.org). With the help of the EDICTOR tool, the data were then annotated for partial cognancy. EDICTOR simplifies not only the annotation of partial cognates but also allows to add information on individual morphemes in the form of so-called morpheme glosses—short glosses, by which the basic meaning or function of individual morphemes can be characterized for the purpose of historical language comparison [We constructed a comparative database of a total of 26 Pano language varieties. This database contains lexical data based on concept list of 181 items (including 25 concepts related to the body). These data were automatically pre-processed by converting the tabular data that had been originally collected into long-table formats that are required by the LingPy software package ,10 and ttalogue  and M(formative), with 26 rows and 26 columns, in which each entry represents the aggregated Hamming distances between a pair of language varieties. With this, we compare both distributions of pairwise distances using a histogram. We used a t-test, implemented in SciPy [To serve as a first quantitative approach to the variability displayed by the morphological structure of body parts in the Pano family, using root and formative-based representations, we developed a simple exploratory analysis based on the Hamming distance . The feain SciPy , to quanSecond, to assess the relative prevalence of the cognate sets in each dataset, we calculated the number of languages contained in each cognate set. Cognate sets that connect many languages will likely derive from a deep branch in the tree, and are therefore useful for recovering the deeper structure in the phylogeny. By contrast, smaller cognate sets that connect fewer languages will tend to be more recent innovations that are therefore useful for refining the fine structure of the tree topology.sklearn library [Third, we applied a principal component analysis (PCA) to the distance matrix M, in order to visualize the overall similarity in the roots and formatives for the internal organization of the Pano family. This method allows us to represent languages in a two-dimensional space, in which location proximity indicates languages with a closer body-part morphological structure (in terms of roots and formatives). We used the PCA implementation of the  library .We finally calculate and plot δ scores ,38 for b. 3. 3.1U-test  confirms this observation. Thus, based on these results, we conclude that roots are more similar lexically and phonetically across languages 1To quantitatively measure the differences between root and formative-based representations of morphological structure of the Pano family, we look at the distribution of the (average) Hamming distance between any pair of languages. On average root-based distances are shorter than formative-based distances: mean root-based distances = 0.14 (s.d. = 0.089) versus mean formative-based distances = 0.17 (s.d. = 0.0829). A Mann–Whitney U-test  and is plotted in Next, we quantify the size of cognate sets in the dataset (i.e. how many languages does each cognate set contain?). We find that, on average, roots connect more languages in a given cognate set: median root size = 2.5 (s.d. = 9.75) versus median formative size = 1 (s.d. = 6.84). This difference is significant under a two-tailed Mann–Whitney . 3.2To gain deeper insight into the internal organization of the morphological structure of body-part terminology among Pano languages, we describe the low-dimensional representation of the root and formative-based distance matrices using PCA . The fig. 3.3At this stage, the radically different story of roots and formatives in body-part terms becomes clear. Roots are less internally variable (i.e. more stable) than formatives . Furthermore, we find significant differences in how languages cluster together when they are viewed as root-based and formative-based low-dimensional representations . Although these results are suggestive of some possible diachronic scenarios, it is necessary to further explore the phylogenetic behaviour of each set of forms in order to arrive at any definitive interpretation. Aiming to test the tree-likeness of body-part roots and body-part formatives we calculated δ scores ,38 for t. 4. 4.1hana ‘tongue’, for instance, which comes from the combination of a body-part root han- and the formative -a, is systematically attested (with predictable sound variation) in all the languages of the family. In cases like this, it is out of question that the protolanguage had already lexicalized the form *hana. At this stage, however, we cannot totally leave out the possibility that *hana ‘tongue’ was indeed originally a monomorphemic word Our quantitative experiments demonstrate that body-part roots are more conservative than body-part formatives, which are often innovative and can be attributed to specific language(s) within the family. The instability of formatives is likely behind their low tree-likeness. This, however, does not mean that the processes of body-part lexicalization postulated here happened at once. Although it is true that a good number formatives were recruited by independent languages in a relatively recent period , some lexicalized body-part terms can be traced up to the protolanguage. The form hana ‘tongue’ is not unique. Indeed, the form taɨ, which might be analysed as the combination of the body-part root ta- and the formative -ɨ, is also attested in all the Pano languages in our sample and therefore *taɨ is also unequivocally a proto-form. A similar situation is found in association with other lexicalized forms, which are attested in several languages from various branches: βɨ-ru ‘eye’ (attested in 23 languages), *ʂɨ-ta ‘tooth’ (attested in 22 languages), *rɨ-kin ‘nose’ (attested in 19 languages), *in-a ‘tail’ (attested in 18 languages), *pɨ-i ‘feather’ (attested in 18 languages) and *ki-ʃi ‘upper leg’ (attested in 16 languages). Although some of these forms might have been originally monomorphemic (Cf. *hana ‘tongue’ and *taɨ ‘foot’), other forms like *ʂɨ-ta ‘tooth’ or *rɨ-kin ‘nose’ fully satisfy the definition of lexicalized form, and thus constitute evidence that the lexicalization process that gave rise to (some) body-part terms in Pano started relatively early.The form *mëkën (Amawaka), mëdante (Matses), mëbi (Shanenawa); or ‘nose’ rëkin (Kapanawa), rëxan (Matis), rëchoko (Yaminawa)).At least some of the lexicalization processes that shape the evolution of body-part terminology in Pano happened in the protolanguage before it began to diverge. This necessarily implies that the construction in which a monosyllabic body-part root was combined with extra morphological material  was productive in a very early stage of the development of the Pano lineage. Therefore, it may have been inherited by modern Pano languages, thus providing the construction frame for future innovative lexicalizations based on conservative roots. Innovative lexicalizations seem to be abundant and this explains the non-tree-like nature of formatives, which are in constant renovation and change. This is why, as explained, while body-part roots are reflected by cognate sets that are largely invariant, body-part formatives may show a great degree of variation  eye, face’ participates in lexicalized body-parts like: bɨ-ru ‘eye’, bɨ-un ‘tear’, bɨ-s¸ha ‘rheum’, bɨ-mana ‘face, forehead, front’, bɨ-bun ‘in front of’. The lexicalization processes described here have to do with the development of new terms as a strategy to denote more specific body parts and related concepts.A question that still remains open would be why body-part roots became combined with extra morphological material to produce new terms in the first place. This seemingly has to do with the need to refer to specific body parts. One of the challenges in the study of body-part terms has to do with the clear delimitation of their semantics . Pano bkin (< kini ‘hole’), -ʂa∼-ʂka (< ʂaka ‘skin’), ʂu , puku (< puku ‘belly’), manan (< manan ‘upper part’) and probably -iwi . Note that in some cases the formative is a reduced version of the original form, but this is not surprising, since synchronic body-part prefixes (which come from body-part roots), may reduce the form of some roots when attached to them [A further question would then have to do with the origin of the formatives involved in these lexicalization processes. Most of these formatives are currently non-productive and exhibit an opaque semantic value. This, however, was not necessarily the case when the morphological process from which most body-part terms evolved was fully productive. Although most formatives remain semantically enigmatic, some of them can be attributed to nominal expressions, as is the case with - to them . Formati. 5. 5.1It is well-known that a relatively clear-cut criterion for distinguishing Western and Eastern Amazonian languages has to do with their overall morphological profile . More sp. 5.2Since early approaches to historical linguistics, shared innovations were considered the gold standard for language clustering and tree topologies. Shared innovations are innovations that occurred in a stage that precedes language splitting, so they are likely to be inherited by the resulting linguistic varieties. Not all innovations, however, are ‘shared’ in the sense just specified. The possibility of finding the same innovation in two or more related languages as the result of independent processes is also a possibility making the task of clustering languages based on innovations a non-trivial one.ma ‘related to head/upper area’ + puku ‘belly’ which seems to be the etymology of modern term mapu ‘head’, the motivation may be found in the round shape that heads and bellies share. On the other hand, if one uses the compound ma ‘related to head/upper area’ + xaka ‘skin’ which seems to be the etymology of modern maxka ‘head’, then the motivation comes from the fact that heads are covered by skin. Such motivated compounds that lexicalized into modern terms for ‘head’ in various Pano languages can easily have happened in two or more varieties independently. As Pano body-part terminology seems to demonstrate, motivated compounds like the ones associated with some of the body-part terms in Pano seem to be more amenable to parallel development. This fully coincides with one of the major findings of this paper: according to their δ scores, Pano body-part formatives are poorly tree-like. Pano body-part terminology may, thus, be a productive domain to test hypotheses regarding the nature of grammatical innovations and their role in language classification, but also proves that δ scores may be recruited to distinguish between shared and parallel innovations in comparative databases.This study demonstrates that in the process of coining body-part terms in Pano, so-called body-part formatives exhibit a complex and diverse chronology and that indeed a good number of them are innovative. Nevertheless, they are less tree-like in terms of their distribution and internal structure, thus suggesting that although they may be attested in two or more languages, they do not satisfy the expectations that one would have for shared innovations. Why, then, did the process of coining body-part terms through innovative morphological combinations trigger so many instances of ‘false’ shared innovations? One possible answer to this question that may provide interesting insights into the nature of linguistic innovations may relate to the origin of the formatives. As argued in §5.2, at least some of these formatives clearly come from nouns, thus suggesting that the various instances of synchronic body-part terms were indeed nominal compounds. The crucial point here is that these compounds are not totally arbitrary. If one uses the compound . 5.3In this paper, we use various statistical methods to demonstrate that body-part roots are generally conservative traits that can be attributed to the protolanguage, while formatives exhibit diverse chronologies, being the case that a number of them are the result of recent and parallel innovations. Language-family-specific traits are usually ignored in quantitative phylogenetic studies. The independent analysis of body-part roots and body-part formatives led us to argue that they exhibit different levels of tree-likeness and therefore cope in different degrees to the understanding of Pano phylogeny. The use of family specific traits proves to be significant for phylogenetic studies. Our results suggest that body-part roots are expected to provide a better classification of Pano languages than body-part formatives, and crucially this is exactly the case as shown in . 6Here we have explored the complex diachronic story of body-part expressions in Pano languages using both quantitative methods and analytical tools from historical linguistics. Body-part expressions in Pano languages are often lexicalized forms, composed by monosyllabic bound roots and semantically opaque morphological formatives. We have demonstrated here that body-part roots and body-part formatives exhibit different diachronic trends: body-part roots are generally conservative forms that can be attributed to the protolanguage, while formatives exhibit a diverse historical signal in the sense that some are retentions from the protolanguage, but a good number of them are recent and parallel innovations in one or a few languages. The diachronic nature of the formatives is behind their highly non-tree-like nature. Based on these results, we provided a full diachronic account of body-part expressions, arguing that while body-part root are generally retentions from the protolanguage, lexicalized body-part terms, which combine roots and formatives, evolved throughout a large period of time. Lexicalized body-part expressions come from a body-part noun compounding process, which was already productive in the protolanguage (see ). Our re


Extracting detailed information from remote sensing images is an important direction in semantic segmentation. Not only the amounts of parameters and calculations of the network model in the learning process but also the prediction effect after learning must be considered. This paper designs a new module, the upsampling convolution-deconvolution module (CDeConv). On the basis of CDeConv, a convolutional neural network (CNN) with a channel attention mechanism for semantic segmentation is proposed as a channel upsampling network (SCU-Net). SCU-Net has been verified by experiments. The mean intersection-over-union (MIOU) of the SCU-Net-102-A model reaches 55.84%, the pixel accuracy is 91.53%, and the frequency weighted intersection-over-union (FWIU) is 85.83%. Compared with some of the state-of-the-art methods, SCU-Net can learn more detailed information in the channel and has better generalization capabilities. Remote sensing image processing technology has developed rapidly. The image semantic segmentation approach based on CNN has become a hot research direction in satellite remote sensing image semantic segmentation , and it Recently, the deep learning method has performed well in the computer vision recognition task, and CNN has achieved very good results in image classification –9, semanThere are many important methods of image processing, among which image semantic segmentation is one. Semantic segmentation is to divide the pixels in the image and predict the category of each pixel in the image using the neural network , which iInspired by these studies, this paper proposes a new method for semantic segmentation of satellite remote sensing images. In the task of semantic segmentation of satellite remote sensing images, the improved upsampling method proposed in this paper not only reduces the number of model parameters but also improves the recognition ability of the model. Based on the new upsampling module, a novel image semantic segmentation model and introduced attention mechanism are proposed. In addition, a new remote sensing image dataset is provided, which shows the remote sensing information of Chenzhou, China. These satellite remote sensing images come from China's GF-2 satellite with a spatial resolution of 0.8 meters, showing various spatial information of cultivated land, forest land, waters, buildings, etc. The original images in the dataset are labeled based on local geomorphological features. Finally, the method in this article was tested on this dataset. Compared with other semantic segmentation methods based on deep learning, SCU-Net has better segmentation performance and stronger generalization ability.This section will, firstly, introduce the structure of FCN. Secondly, the structure and principle of SCU-Net proposed in this paper are introduced. Finally, the network complexity of SCU-Net is analyzed through experiments.The main difference between the FCN network and the traditional deep learning convolutional network is that it does not use a full connection layer. The FCN network adds an upsampling method to the network structure. The output image has the same size as the original input image, which realizes pixel classification. FCN is mainly composed of the feature extraction module of the ordinary convolutional network, upsampling, and skip connection. H × W, the original image will be reduced to (H × W)/2 after the “Conv1” and “MaxPooling” operations. Then, the feature map is reduced to (H × W)/4 through the operations of “conv2” and “MaxPooling.” By using the “Conv3” and “MaxPooling” operations, the output feature map “featureMap-3” with reduced size (H × W)/8 can be obtained. Then, “Conv4” and “MaxPooling” operations are performed to reduce the size of the feature map to (H × W)/16, and the output feature map is named “featureMap-4.” In the next step, the feature map goes through “Conv5” and the last “MaxPooling” operation, and the feature map, namely “featureMap-5,” will be reduced to (H × W)/32.The first operation is feature extraction. If the input image size is H × W)/8. Next, “featureMap-5” performs the “Upsampling-2” operation to obtain the feature map “featureMap-7” whose size is (H × W)/8. Then, “featureMap-6” and “featureMap-7” are stitched together. Finally, the “Upsampling-3” operation is performed on the output result to output the feature map. The size of this feature map is the same as the original image, and the semantic segmentation is completed.After the feature extraction is completed, the upsampling operation is performed. First, the “Upsampling-1” operation is performed on “featureMap-4” to obtain a feature map “featureMap-6” with a size of  is introdThe CFWE module is a multilayer structure. The first is the short connections layer of the CFWE. It contains 3 convolutional layers, of which, there are two conv1 and one conv3. The two “conv1” in the module are used to increase and decrease the number of channels, respectively, with the purpose of reducing the amounts of parameters. The shortcut connections layer can alleviate the network degradation problem to a certain extent. Next comes the serial pool layer and full connection layer structure, which consists of two “FC” structures and a “GAP” structure. Firstly, the feature map of each channel is processed as a global feature using the “GAP” structure. Then, the feature dimension is reduced through the first “FC” layer, and the feature dimension is restored by the second “FC” layer. The weight coefficient model of each channel can be learned after passing through two “FC” layers. Finally, the final output feature map is to multiply the original feature and the extracted feature map channel weight coefficients by short connections. When extracting features, the weight coefficient is useful for the model to extract more important channel features and then enhance the feature extraction ability of the network.In the traditional semantic segmentation neural network, the upsampling step is divided into two steps. Firstly, the feature map size is up-sampled to the original image size, and then point convolution is performed to complete the semantic segmentation. The parameters and calculations of the network model using this method are relatively large. The “CDeConv” module proposed, firstly, performs point convolution to make the number of feature map channels consistent with the number of segmentation task categories, and then, it performs deconvolution to make the output feature map size consistent with the original image size. This module not only reduces the number of model calculations and parameters but also improves model performance. Its structure is shown in k equal to 7 and a stride equal to 2. “Conv1” is a “Conv” structure with k equal to 1 and a stride equal to 1. “Conv1-3-1” is a structure consisting of “Conv1,” “Conv3,” and “Conv1” in series. One of the two “Conv1” structures is used to increase the dimensionality and the other can decrease the dimensionality. This operation can reduce the complexity of the model. “Conv3” is used for feature extraction. “Maxpooling” means the maximum pooling layer with a step size of 2 and a window size of 3. Its main function is to upsample, reduce dimensionality, and reduce the amount of calculation. “Upsampling” represents an 8 times upsampling module, and its function is to upsample the feature map to the same size as the original image to achieve semantic segmentation.According to the CFWE module and the “CDeConv” module, a novel semantic segmentation network model SCU-Net is proposed, whose structure is shown in X and the size is H × W × 3, it, firstly, passes through the “Conv7” module with 64 convolution kernels. The step size is 2, and the convolution kernel size is 7. Set the output feature map of the “Conv7” module to X1. The size becomes H/2 × W/2 × 64, which is shown as follows:If the input image is X2 will become 0.25 times that of X1, as shown below.After a maxpool layer, the number of channels will not change, however, the size of the output feature map n  serially connected “Conv1_3_1,” the output size of the feature map is H/4 × W/4 × 256. Next, the output X3 can be obtained by using CFWE module. Its feature map size is H/4 × W/4 × 256, which can be expressed as follows:Then, through X3 is input to the n series of “Conv1_3_1” modules, and then through a layer of CFWE module, the output feature map X4 has a size of H/8 × W/8 × 512, which can be expressed as follows:After that, the feature map X4 is input to the n series of “Conv1_3_1” modules, and then through a layer of CFWE module, the output feature map X5 size is H/16 × W/16 × 1024, which can be expressed as follows:The feature map X5 is input to n serially connected “Conv1_3_1” modules, and the output feature map X6 has a size of H/32 × W/32 × 2048, which can be expressed as follows:Then, the feature map X6 uses a CDeConv module to perform point convolution, firstly, to achieve the purpose of reducing the number of channels, reducing the number of channels to 7. Then, upsample 4 times, and get the output X7. Its feature map size is H/8 × W/8×7, which can be expressed as follows:The feature map X5 enters a CDeConv module through a skip connection. Firstly, point convolution is performed to reduce the number of channels to 7. Then, upsample 2 times. Get the output X7′. Its feature map size is H/8 × W/8 × 7, which can be represented as follows:Feature map X4 reduces the number of channels to 7 through a point convolution, and the size of the output feature map X7″ is H/8 × W/8 × 7, which can be represented as follows:The feature map X7, X7′, and X7″ bit-by-bit to get X8. Its feature map size is H/8 × W/8 × 7, which can be expressed as follows:Then, add X8 passes an 8 times upsampling module to output the final output feature map, whose size is H × W × 7, and can be expressed asThe final feature map Three different upsampling methods using different numbers of “CDeConv” modules and skip connections are designed. Based on SCU-Net, combined with data expansion technology for image preprocessing, an automatic remote sensing image segmentation method is proposed. Model complexity refers to the amount of calculation and parameters of the network. The parameters and calculations of different upsampling methods and depth models are compared through the experiments. Experiments were performed with one “CDeConv,” two “CDeConv,” and three “CDeConv” modules in the network model using three different upsampling methods. By combining three different upsampling methods and three different network depths, we can get 9 different network models. As shown in The floating point of operations refers to the number of multiplication and addition operations in the model. As shown in This experimental dataset comes from the fusion image of GF-2 in the Chenzhou area in 2016. As shown in Firstly, set the dataset image to the output image of the specified size as needed.Secondly, perform random window sampling with a window size of 256 × 256 on the image, i.e., randomly generate sampling coordinates, and then obtain an image with a size of 256 × 256 under the coordinates.Finally, data enhancement is performed on the segmented images, and image transformation operations are performed, such as rotation, vertical flipping, horizontal flipping, blurring, corrosion, random gamma transformation, bilinear filtering, and adding noise at random.In the deep learning network, it is easy to cause memory overflow when large remote sensing images to be classified are directly input into the network model. It is difficult for the model to identify the original data without preprocessing. Furthermore, training a deep learning network model needs lots of training data, however, labeling geographic information in satellite remote sensing images is a very complicated and time-consuming task, and labor costs are too high, making it difficult to produce large datasets. Additionally, for avoiding overfitting because of the small amount of data in the training data set in the process of deep learning neural network training, the existing training set needs to be enhanced and expanded. The image sizes of high-resolution remote sensing datasets are also inconsistent. Therefore, for a high-resolution remote sensing image, it needs to be cut into small images of uniform size as an experimental dataset. The pretreatment process is as follows:After the above data preprocessing and data expansion, the amount of data in the training set has become 6 times that of the original dataset, which reduces the risk of network overfitting in a way.To ensure the reliability of the performance comparison of different network models, the experiments in this paper are carried out under the same development platform and hardware environment. The experimental equipment system is Windows 10, CPU  is Intel i7 3.30 GHz, GPU (graphics processing unit) is GeForce GTX 1080Ti (11G), GPU environment is CUDNN 10.0 and CUDA 10.0, the development platform is PyCharm, the programming language is Python, and the framework is Pytorch. The batch size of the test set is 4, and the batch size of the training set is also 4.K + 1. The formulas of PA, MIOU, and FWIU are as follows:There are a variety of evaluation criteria used in semantic segmentation models. The evaluation criteria adopted in this paper are those adopted by most semantic segmentation models, including frequency weighted intersection (FWIU), pixel accuracy (PA), and mean intersection (MIOU) as performance indicators . The evaPii represents the number of class i pixels that are correctly classified, and Pij represents the number of class i pixels classified as class j.Among them, i. TN is defined as the negative sample predicted correctly by the model. Defining FP as a negative sample is incorrectly predicted by the model to be a positive sample. Define FN as the class i is predicted to be other classes. Then, the precision is defined as follows:In addition, the precision, recall, and F1-score indicators in image classification are used in the experiment to evaluate the prediction effect of a single category. TP is defined as the model correctly predicted class Recall is defined as follows:F1-score is defined as the harmonic mean of precision and recall, which is as follows:In this paper, nine kinds of SCU-Nets are designed and tested on the dataset. The effect of depth and upsampling methods on the segmentation performance of SCU-Nets is studied. The experimental results are displayed in According to the above table, the performance of SCU-Net using the C structure as the upsampling method is lower than the model using the other two structures. SCU-Net-102-A has the best comprehensive performance in the dataset. PA and MIOU are the highest, i.e., 91.53% and 55.84%, respectively. The MIOU of SCU-Net-102-A is the highest, which is 55.84%. It is 0.95% and 1.43% higher than SCU-Net-51-A and SCU-Net-153-A individually.The results show that the depth of SCU-Net should be moderate, while scaling shallower or deeper may cause the performance of the network model to decrease. Meanwhile, SCU-Net-51-A is compared with other networks for studying the influence of parameters on network performance. Further comparisons are also conducted with the classic semantic segmentation neural networks DeepLab, U-Net, SegNet, FCN, Dilated, and the most recent networks FC-DenseNet and DFCN121. For the model obtained when the CFWE module in SCU-Net-102-A was deleted, a comparative experiment was carried out to verify the effectiveness of the CFWE module. The experimental comparison results are shown in As can be seen from the above table, SCU-Net-102-A without a CFWE module is significantly lower than that of SCU-Net-102-A with CFWE module, and the parameters of the three CFWE modules are only 10,000. Hence, it can be inferred that the CFWE module has very few parameters and can greatly improve the performance of SCU-Net. DeepLabV3 uses and improves the ASPP module, which has a good effect on the GF-2 dataset, however, the performance is still lower than SCU-Net, and DeepLabV3 has many more model parameters than SCU-Net-102-A. FCN-8s achieved pixel classification by abandoning the fully connected layer of the traditional neural network and made great success on the GF-2 dataset with very few parameters. SegNet is a semantic segmentation network that improves VggNet-16 and is based on the FCN network. At the same time, it introduces the encoder-decoder structure, which has achieved good results on the GF-2 dataset, and the number of parameters is more than SCU-Net-51-A. U-Net was put forward to settle the matter of semantic segmentation of medical images. A U-shaped network structure was proposed to obtain location information and context information simultaneously. Although the parameters of U-Net are very few, it performs poorly on the GF-2 dataset. FC-DenseNet and DFCN121 introduced DenseNet into the model of semantic segmentation. At the same time, regardless of the number of other network parameters, SCU-Net performance is better than theirs. SCU-Net-51-A has low parameters and high performance. It shows that SCU-Net has better performance and lower model complexity and can be more targeted to complete the task of semantic segmentation of satellite remote sensing images.To evaluate the application effect of the network in actual remote sensing images, use 2000 remote sensing images of 256 × 256 size as a test. It can be seen from The experimental results show that the PA and MIOU of SCU-Net-102-A are the highest, which are 91.53% and 55.84%, respectively. After comprehensive consideration, SCU-Net-102-A is chosen to compare with other typical semantic segmentation networks and the more recent semantic segmentation networks. It is found that the comprehensive performance of the network is better than other networks. Judging from the experimental results, the network depth should be kept appropriate in the task of semantic segmentation of satellite remote sensing images. Too few network layers make it difficult to extract sufficient features, and too many network layers will cause vanishing gradient problem or gradient explosion problem. The problems of gradient dispersion and gradient explosion can be solved to some extent by batch normalization, and the degradation problem can be alleviated by jumping connection. The CDeConv upsampling module uses a point convolutional layer, which improves the feature extraction capability of the network on the basis of reducing the number of network parameters. In addition, the attention mechanism module CFWE module, which uses skip connections to settle the matter of network degradation to some extent, is introduced. Simultaneously, the CFWE module learns the channel weight coefficients using the attention mechanism, which enhance the feature extraction capability of the network and achieves a better image segmentation effect. SCU-Net-102-A and DFCN121C networks are selected for experiments to compare and predict the effects of different categories. The precision of the SCU-Net-102-A model for forest land prediction is 97.10%, and the recall is 93.42%. The corresponding F1-scores reached 0.952, which is the best among the 7 classes, and these three values are higher than those of the DFCN121C model. At the same time, all kinds of F1 scores predicted by SCU-Net-102-A are higher than those predicted by DFCN121C, except for the “others” class. Combined with the experimental results, it can be proved that SCU-Net-102-A is better than DFCN121C in predicting each.The visualization diagram of the SCU-Net-A test output is shown in On the whole, the prediction effect of SCU-Net-102-A is better than the image predicted by DFCN121C. In the first raw image, the waters are marked as bare ground because of human labeling errors. Both SCU-Net-A and DFCN121C can correctly predict waters, however, it is clear that SCU-Net-102-A understands the details better, as shown by the yellow boxes in the first column of This paper proposes a new semantic segmentation model for high-resolution remote sensing images based on CNNs. A new upsampling module CDeConv is proposed in this network model, and the attention module CFWE is used to improve the feature extraction ability of the network. In the experiment of this paper, the GF-2 satellite remote sensing image of Chenzhou in 2016 is used, and the ground truth was labeled manually. Finally, there were 7 categories of classified objects in the dataset. By analyzing the experimental results, it is concluded that SCU-Net-102-A has the highest value, and its PA and MIOU are 91.66% and 55.61%, respectively. The precision of SCU-Net-102-A for woodland prediction is 97.10%, and the corresponding F1-score is 0.952, which is the highest F1-score among the seven categories. It can achieve accurate segmentation of complex targets in GF-2 image classification tasks. The model designed in this paper is designed to detect the changes in forest land and water area in Chenzhou, China, and to provide help for the protection and development of forest and water environment. It is hoped that more satellite remote sensing images of the same kind can be obtained in the future, and higher-quality segmentation datasets can be generated to further train SCU-Net to improve its versatility and segmentation performance.


Parkinson's disease is mainly characterized by clinical motor manifestations, with postural instability being a predominant symptom that leads to many falls. One way in which postural control is assessed is to measure the characteristics of postural sway during quiet standing. In this test, subjects standstill on a force platform, which records ground forces and reaction moments that can be used to calculate the center of pressure (CoP) . Inclusion criteria were the absence of neurological or physical dysfunctions other than those associated with PD and no diagnosed vestibular, visual, or somatosensory dysfunctions as self-declared.A convenience sample of 32 idiopathic PD patients  was recruited to participate in this study. The patients were recruited from local communities and included local neighborhoods and ambulatory movement disorders. The patients were interviewed to collect information about their demographic characteristics, socio-cultural characteristics, and overall health condition. Their ages varied from 44 to 81 years, body masses from 53.3 to 95.6 kg, heights from 151.5 to 184.0 cm, body-mass indexes (BMI) from 17.5 to 31.5 kg/mThe stabilography evaluation was based on the most common practices used in research laboratories . The patient's feet were positioned on the marks at the force platform or on the foam blocks. The researcher instructed the patient to maintain the position of his or her arms along his or her body and to stand as still as possible. During the trials, with the patient's eyes open, the patients were told to fix their gaze ahead on the round black target placed on the wall at the patient's eye level. During the trials with eyes closed, the patients were told to fix their gaze ahead at the same target, close their eyes when they felt ready, and only open them when the researcher indicated that the trial was over.The researcher started the data collection around 5 s later when the patient said he or she was ready.At the end of the trial, the subject was assisted to step from the force platform, and he or she could rest (and sit if desired) for about one minute before the subsequent trial.If the subject was unable to complete a 30 s trial, the test was stopped.The force platform data were smoothed with a 10 Hz fourth-order zero-lag low-pass Butterworth filter, and the center of pressure (CoP) was calculated according to the standard formula ; the data is stored in ASCII (text) format with tab-separated columns that can be downloaded as a single compressed file that is made available under the CC0 1.0 license (https://creativecommons.org/publicdomain/zero/1.0/). The data set comprises a file with metadata plus 767 files with the GRF for the 32 patients in each medication condition.All the data is available at Figshare ; XX identifies the patient and varies from 01 to 32.Gender: gender (F or M).Age: patient's age in years.Height (cm): height in meters .Weight (kg): weight in kilograms .2): body mass index in kg/m2.BMI (kg/mOrtho-Prosthesis: name of the orthosis or prosthesis the subject wears (“No” if the patient did not wear any orthosis or prosthesis).Years of formal study: years of formal education.Disease duration (years): year from diagnosis.−1): total daily levodopa equivalent dose in mg•day−1 according to Tomlinson et al.  or not (non-freezers) of freezing of gait.NFoG-Q (score): score of New Freezing of Gait Questionnaire.PIGD or TD: Postural Instability/Gait Difficulty (PIGD) or Tremor Dominant (TD) phenotypes of Parkinson's disease according to Stebbins et al. .Initial symptoms: self-reported initial symptoms.Is there a family history of PD? Who?Do you feel improvement after using the antiparkinsonian medicine?: Yes or No.Have you ever had any surgery? Which?Any rehabilitation or physical activity?: name of the rehabilitation or physical activity performed by the patient .Other diseases : name of the disability of the patient (“No” if the patient did not present any disability).ON—Hoehn & Yahr: Hoehn & Yahr score in the ON medication.ON—MoCA: MoCA score in the ON medication.ON—UPDRS-II: total score of the UPDRS-II in the ON medication.ON—UPDRS-III: total score of the UPDRS-III in the ON medication.ON—UPDRS-III—Rigidity: score of item 5—rigidity of UPDRS-III in the ON medication.ON—UPDRS-III—Gait: score of item 12—rigidity of UPDRS-III in the ON medication.ON—UPDRS-III—Bradykinesia: score of item 14—bradykinesia of UPDRS-III in the ON medication.ON—UPDRS-III—Dyskinesia: score of item 15—dyskinesia of UPDRS-III in the ON medication.ON—miniBESTest: miniBESTest score in the ON medication.ON—FES-I: FES-I score in the ON medication.OFF—Hoehn & Yahr: Hoehn & Yahr score in the OFF medication.OFF—MoCA: MoCA score in the OFF medication.OFF—UPDRS-II: total score of the UPDRS-II in the OFF medication.OFF—UPDRS-III: total score of the UPDRS-III in the OFF medication.OFF—UPDRS-III—Rigidity: score of item 5—rigidity of UPDRS-III in the OFF medication.OFF—UPDRS-III—Gait: score of item 12—rigidity of UPDRS-III in the OFF medication.OFF—UPDRS-III—Bradykinesia: score of item 14—bradykinesia of UPDRS-III in the OFF medication.OFF—UPDRS-III—Dyskinesia: score of item 15—dyskinesia of UPDRS-III in the OFF medication.OFF—miniBESTest: miniBESTest score in the OFF medication.OFF—FES-I: FES-I score in the O OFF medication.Each text file with the GRF data is named by the corresponding condition and trial . The header refers to the signal at each column and are:Time: Time in s.GRFml [N]: mediolateral Ground Reaction Force (GRF) in N.GRFap [N]: anteroposterior GRF in N.GRFv [N]: vertical GRF in N.Mml [N.m]: mediolateral moment of force in N.m.Map [N.m]: anteroposterior moment of force in N.m.Mml [N.m]: vertical moment of force in N.m.Mfree [N.m]: Free Moment at the direction Y in Nm.CoPml [m]: mediolateral center of pressure in m.CoPap [m]: anteroposterior center of pressure in m.https://doi.org/10.6084/m9.figshare.13530587).This study provides a publicly available data set with qualitative and quantitative evaluations related to the balance of PD patients. All the data is available at Figshare  can be found in the article/supplementary material.The studies involving human participants were reviewed and approved by Federal University of ABC. The patients/participants provided their written informed consent to participate in this study.CO: conceptualization, methodology, data collect, writing—original draft, and writing—review and editing. CR: conceptualization, methodology, data collect, and writing—original draft. RT, SH, EL, CB, TS, LS, TN, DC, and EG: methodology and data collect. MC: methodology, data collect, and writing—review and editing. DBC: conceptualization, methodology, data collect, writing—original draft, writing—review and editing, and supervision. All authors contributed to the article and approved the submitted version.This study was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP/Brazil)—grant #2019/06604-1, Universidade Federal do ABC (UFABC/Brazil), and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES/Brazil).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.