
Nanofiber mats can be produced by electrospinning from diverse polymers and polymer blends as well as with embedded ceramics, metals, etc. The large surface-to-volume ratio makes such nanofiber mats a well-suited substrate for tissue engineering and other cell growth experiments. Cell growth, however, is not only influenced by the substrate morphology, but also by the sterilization process applied before the experiment as well as by the chemical composition of the fibers. A former study showed that cell growth and adhesion are supported by polyacrylonitrile/gelatin nanofiber mats, while both factors are strongly reduced on pure polyacrylonitrile (PAN) nanofibers. Here we report on the influence of different PAN blends on cell growth and adhesion. Our study shows that adding ZnO to the PAN spinning solution impedes cell growth, while addition of maltodextrin/pea protein or casein/gelatin supports cell growth and adhesion.
Citation: Daria Wehlage, Hannah Blattner, Al Mamun, Ines Kutzli, Elise Diestelhorst, Anke Rattenholl, Frank Gudermann, Dirk Lütkemeyer, Andrea Ehrmann. Cell growth on electrospun nanofiber mats from polyacrylonitrile (PAN) blends[J]. AIMS Bioengineering, 2020, 7(1): 43-54. doi: 10.3934/bioeng.2020004
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[2] | Miao Peng, Rui Lin, Zhengdi Zhang, Lei Huang . The dynamics of a delayed predator-prey model with square root functional response and stage structure. Electronic Research Archive, 2024, 32(5): 3275-3298. doi: 10.3934/era.2024150 |
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[8] | San-Xing Wu, Xin-You Meng . Hopf bifurcation analysis of a multiple delays stage-structure predator-prey model with refuge and cooperation. Electronic Research Archive, 2025, 33(2): 995-1036. doi: 10.3934/era.2025045 |
[9] | Jiange Dong, Xianyi Li . Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting. Electronic Research Archive, 2022, 30(10): 3930-3948. doi: 10.3934/era.2022200 |
[10] | Chen Wang, Ruizhi Yang . Hopf bifurcation analysis of a pine wilt disease model with both time delay and an alternative food source. Electronic Research Archive, 2025, 33(5): 2815-2839. doi: 10.3934/era.2025124 |
Nanofiber mats can be produced by electrospinning from diverse polymers and polymer blends as well as with embedded ceramics, metals, etc. The large surface-to-volume ratio makes such nanofiber mats a well-suited substrate for tissue engineering and other cell growth experiments. Cell growth, however, is not only influenced by the substrate morphology, but also by the sterilization process applied before the experiment as well as by the chemical composition of the fibers. A former study showed that cell growth and adhesion are supported by polyacrylonitrile/gelatin nanofiber mats, while both factors are strongly reduced on pure polyacrylonitrile (PAN) nanofibers. Here we report on the influence of different PAN blends on cell growth and adhesion. Our study shows that adding ZnO to the PAN spinning solution impedes cell growth, while addition of maltodextrin/pea protein or casein/gelatin supports cell growth and adhesion.
Recently, using Solodov and Svaiter's projection technique [1], several conjugate gradient methods for solving large-scale unconstrained optimization problems have been extended to solve nonlinear equations with convex constraints (see, [2,3,4,5,6,7,8,9] and the references therein). Due to its simplicity, low storage requirement, and applications, the method has been of interest to various research communities [10,11,12,13,14]. As known, the Fletcher-Reeves (FR) [15], Conjugate Descent (CD) [16] and Dai-Yuan (DY) [17] conjugate gradient methods have strong convergence properties, but due to jamming, they do not do well in practice. Having said that, the Hestenes-Stiefel (HS) [18], Polak-Ribiére-Polyak (PRP) [19,20], and Liu-Storey (LS) [21] conjugate gradient methods do not necessarily converge, but they often work better than FR, CD and DY. In [22], in order to combine the numerical efficiency of the LS method and the strong convergence of the FR method, Djordjević proposed a hybrid LS-FR conjugate gradient method for solving the unconstrained optimization problem. In her work, the conjugate gradient parameter was computed as a convex combination of the LS and FR conjugate gradient parameter. The hybridization parameter for the convex combination was obtained in such a way that the direction of the proposed method satisfies the condition of the Newton direction but also at the same time, it satisfies the famous Dai-Liao conjugacy condition.
In an attempt to extend the LS-FR method of Djordjević to solve monotone nonlinear equations with convex constraints, Ibrahim et al. [23] proposed a derivative-free hybrid LS-FR conjugate gradient method with a conjugate gradient parameter computed as a convex combination of derivative-free LS and FR conjugate gradient parameter. The hybridization parameter of the convex combination in their work was obtained to satisfy the famous conjugacy condition. Numerical results show that the method is efficient for solving nonlinear monotone equations with convex constraints. It is noteworthy to state that, several conditions were imposed on the hybridization parameter used in [23] in order for the hybridization parameter to take values within the interval (0,1).
Our motivation is the following: Can we extend the LS-FR method proposed by Djordjević to construct an efficient hybrid gradient-free projection algorithm where the hybridization parameter has no condition imposed on it and the hybridization parameter will always take values in the interval [0,1])? In this paper, we give a positive answer to this question. The remainder of the paper is organized as follows. In Section 2, we describe the algorithm and some properties. In Section 3, we analyze the global convergence of the method. Numerical example and application are presented in Section 4 and 5 respectively.
Consider the following unconstrained optimization problem
minimizeg(z),z∈Rn, | (2.1) |
where g:Rn→R is a continuously differentiable function whose gradient at zk is denoted by f(zk):=∇(zk). Given any starting point z0∈Rn, the algorithm in [22] is to generate a sequence of approximation {zk} to the minimum z∗ of g, in which
zk+1=zk+tkjk,k≥0, | (2.2) |
where tk>0 is the steplength which is computed by a certain line search and jk is the search direction defined by
jk={−f(zk)+βkjk−1if k>0,−f(zk)if k=0, | (2.3) |
with βk defined by
βk=(1−θk)f(zk)Tyk−1−f(zk−1)Tjk−1+θk‖f(zk)‖2‖f(zk−1)‖2,yk−1=f(zk)−f(zk−1). | (2.4) |
where θk is a hybridization parameter chosen to satisfy the Dai-Liao's condition, that is, {for t>0,}
jTkyk−1=−tsTk−1f(zk), |
where sk−1=zk+1−zk.
Motivated by (2.3) and (2.4), we propose a gradient free projection algorithm for solving the following nonlinear equation with convex constraints:
ρ(z)=0,z∈Ω | (2.5) |
where Ω⊆Rn is a nonempty closed convex set, and ρ:Rn→Rn is a continuous mapping. Our propose gradient-free projection iterative method first generates a trial point say {ck} using the relation:
ck=zk+tkjk,tk>0, | (2.6) |
the search direction jk is computed by
jk={−ρ(zk)if k=0,−πkρ(zk)+βkwk−1if k>0, | (2.7) |
where βk is computed
βk:=(1−θk)ρ(zk)Tyk−1−ρ(zk−1)Tjk−1+θk‖ρ(zk)‖2‖ρ(zk−1)‖2,θk:=‖yk−1‖2yTk−1w∗k−1,w∗k−1:=wk−1+(max{0,−wTk−1yk−1‖yk−1‖2}+1)yk−1,yk−1:=ρ(zk)−ρ(zk−1),wk−1:=ck−1−zk−1, |
and πk is obtained to satisfy the descent condition, that is, for α>0,
jTkρ(zk)≤−α‖ρ(zk)‖2. | (2.8) |
For k=0, (2.8) obviously holds. For k∈N, we have
ρ(zk)Tjk≤−(πk−βkρ(zk)Twk−1‖ρ(zk−1)‖2)‖ρ(zk)‖2. | (2.9) |
To satisfy (2.8), we only need that
πk≥l+βkρ(zk)Twk−1‖ρ(zk−1)‖2,l>0. | (2.10) |
In this paper, we choose πk as
πk=l+βkρ(zk)Twk−1‖ρ(zk−1)‖2. | (2.11) |
It is important to note that, θk has the following property:
yTk−1w∗k−1≥max{yTk−1wk−1,‖yk−1‖2}≥‖yk−1‖2>0. |
Thus,
θk=‖yk−1‖2yTk−1w∗k−1∈(0,1),∀k.
The definition of w∗k−1 is from the ideas of Li and Fukushima [24,25]. The definition of θk was originally proposed by Birgin and Martinez [26] and similar idea can be found in [27,28] and other optimization literature. The proposed algorithm is described immediately after recalling the definition of the projection operator.
Definition 2.1. Let Ω⊆Rn be a nonempty closed convex set. Then for any x∈Rn, its projection onto Ω, denoted by PΩ[x], is defined by
PΩ[x]:=argmin{‖x−y‖ :y∈Ω}. |
The projection operator PΩ has a well-known property, that is, for any x,y∈Rn the following nonexpansive property hold
‖PΩ(x)−PΩ(y)‖≤‖x−y‖,∀x,y∈Rn. | (2.12) |
Algorithm 1: |
Input. Choose an initial point z0∈Ω, Initialize the variables: τ∈(0,1),η∈(0,2) Tol>0, κ>0,l>0. Set k=0. |
Step 0. Compute ρ(zk). If ‖ρ(zk)‖≤Tol, stop. Otherwise, compute jk by (2.7) |
Step 1. Determine the steplength tk=max{τm|m=0,1,2,⋯} such that |
−ρ(zk+τmjk)Tjk⟩≥κτm‖jk‖2. (2.13) |
Step 2. Compute the trial point ck=zk+tkjk. |
Step 3. If ck∈Ω and ‖ρ(ck)‖≤Tol, stop. Otherwise, compute |
zk+1=PΩ[zk−ημkρ(ck)] (2.14) |
where |
μk=ρ(ck)T(zk−ck)‖ρ(ck)‖2. |
Step 4. Set k:=k+1 and go to step 1. |
In what follows, we assume that ρ satisfies the following assumptions.
Assumption 1. The solution set Ω∗ is nonempty.
Assumption 2. The mapping ρ is Lipschitz continuous on Rn. That is,
‖ρ(x)−ρ(y)‖≤L‖x−y‖,∀x,y∈Rn. |
Assumption 3. For any y∈Ω∗ and x∈Rn, it holds that
ρ(x)T(x−y)≥0. | (3.1) |
Lemma 3.1. Suppose that Assumption 1 holds. Then there exists a step-size tk satisfying the line search (2.13) for k≥0.
Proof. Assume there exist k0≥0 such that (2.13) fails to hold for any i≥0, that is
−⟨ρ(zk0+τijk0),jk0⟩<κτi‖jk0‖2,∀i≥1. |
Applying the continuity property of ρ and letting i→∞ yields
−ρ(zk0)Tjk0≤0, |
which negates (2.8). Hence proved.
Lemma 3.2. Suppose Assumption 1-3 is satisfied and the sequences {zk,ck,tk,jk} are generated by Algorithm 1. Then
tk≥min{1,τ(L+κ)‖ρ(zk)‖2‖jk‖2}. |
Proof. Note that from (2.13), if tk≠1, then ˉtk=τ−1tk does not satisfy (2.13), that is,
−ρ(zk+τ−1tkjk)Tjk<κτ−1tk‖jk‖2. | (3.2) |
Combining the above inequality with the descent condition (2.8), we have
‖ρ(zk)‖2=−ρ(zk)Tjk=(ρ(zk+τ−1tk)−ρ(zk))Tjk−ρ(zk+τ−1tk)Tjk≤τ−1tkL‖jk‖2+τ−1tkκ‖jk‖2=τ−1tk(L+κ)‖jk‖2. | (3.3) |
Since ρ satisfies Assumption 2 then, (3.3) holds. Thus, from (3.3),
tk≥min{1,τ(L+κ)‖ρ(zk)‖2‖jk‖2}. | (3.4) |
This proves Lemma 3.2.
Lemma 3.3. Suppose that Assumptions 1-3 hold and let {zk} and {ck} be the sequences generated by Algorithm 1. Then, ρ(ck) is an ascent direction of the function ‖z−z∗‖2 at the point zk, where z∗∈Ω∗.
Proof. At zk, the function 12‖x−z∗‖2 has a gradient of zk−z∗. By the weakly monotonicity property (3.1), it can be seen that
ρ(ck)T(zk−z∗)=ρ(ck)T(zk+ck−ck−z∗)=ρ(ck)T(ck−z∗)+ρ(ck)T(zk−ck)=ρ(ck)T(zk−ck)≥κt2k‖jk‖2=κ‖zk−ck‖2>0. | (3.5) |
The inequality above, i.e., (3.5) points out that −ρ(ck) is a descent direction of the function ‖z−z∗‖ at the iteration point zk.
Lemma 3.4. Let Assumption 1-3 hold and the sequence {zk} be generated by Algorithm 1. Suppose that z∗ is a solution of problem (2.5) with ρ(z∗)=0. Then there exists a positive δ>0 such that
‖ρ(zk)‖≤δ. | (3.6) |
Proof. Remember, by using the well-known property of PΩ, we can deduce that for any z∗∈Ω∗,
‖zk+1−z∗‖2=‖PΩ[zk−ημkρ(ck)]−z∗‖2≤‖zk−ημkρ(ck)−z∗‖2=‖zk−z∗‖−2ημkρ(ck)T(zk−z∗)+η2μ2k‖ρ(ck)‖2=‖zk−z∗‖−2ηρ(ck)T(zk−ck)‖ρ(ck)‖2ρ(ck)T(zk−z∗)+η2(ρ(ck)T(zk−ck)‖ρ(ck)‖)2≤‖zk−z∗‖−2ηρ(ck)T(zk−ck)‖ρ(ck)‖2ρ(ck)T(zk−ck)+η2(ρ(ck)T(zk−ck)‖ρ(ck)‖)2=‖zk−z∗‖2−η(2−η)(ρ(ck)T(zk−ck)‖ρ(ck)‖)2 | (3.7) |
≤‖zk−z∗‖2. | (3.8) |
From inequality (3.8) we see that {‖zk−z∗‖} is a decreasing sequence and hence {zk} is bounded. That is,
‖zk‖≤a0,a0>0. | (3.9) |
Furthermore, we obtain
‖zk+1−z∗‖≤‖zk−z∗‖≤‖zk−1−z∗‖≤⋯‖z0−z∗‖. | (3.10) |
Using the Lipchitz continuity of ρ, we have
‖ρ(zk)‖=‖ρ(zk)−ρ(z∗)‖≤L‖zk−z∗‖≤L‖z0−z∗‖. | (3.11) |
Setting δ=L‖z0−z∗‖ proves Lemma 3.4.
Lemma 3.5. Suppose Assumption 1-3 hold and the sequence {zk} and {ck} are generated by Algorithm 1. Then,
(a) {ck} is bounded
(b) limk→∞‖zk−ck‖=0
(c) limk→∞‖zk−zk+1‖=0.
Proof. (a) From (3.10), we know that the sequence {zk} is bounded. So by (3.5), we have
ρ(ck)T(zk−ck)≥κ‖zk−ck‖2. | (3.12) |
By (3.1) and (3.6) we have
ρ(ck)T(zk−ck)=(ρ(ck)−ρ(zk))T(zk−ck)+ρ(zk)T(zk−ck)≤‖ρ(zk)‖‖zk−ck‖≤δ‖zk−ck‖. |
Combined with (3.12), it is easy to deduce that
‖zk−ck‖≤δκ. |
Then, we obtain,
‖ck‖≤δκ+‖zk‖ |
Thus {ck} is bounded due to {zk} boundedness.
(b) From inequality (3.7), we get
‖zk+1−z∗‖≤‖zk−z∗‖2−η(2−η)[ρ(ck)T(zk−ck)]2‖ρ(ck)‖2≤‖zk−z∗‖2−η(2−η)κ2‖zk−ck‖4‖ρ(ck)‖2, |
which means
η(2−η)‖zk−ck‖4≤‖ρ(ck)‖2κ2(‖zk−z∗‖2−‖zk+1−z∗‖2). |
Since the mapping ρ is continuous, and the {ck} is bounded, we know that {‖ρ(ck)‖} is bounded. Therefore a positive δ1>0 exists, such that ‖ρ(ck)‖≤δ1 and moreover
η(2−η)∞∑k=0‖zk−ck‖4≤δ21κ2∞∑k=0(‖zk−z∗‖2−‖zk−z∗‖2)=δ21κ2‖z0−z∗‖2<+∞. |
Hence,
limk→∞tk‖jk‖=limk→∞‖zk−ck‖=0. | (3.13) |
Using the property of the projection operator, i.e., (2.12), we have
‖zk−zk+1‖=‖zk−PΩ[zk−ημkρ(ck)]‖≤‖zk−(zk−ημkρ(ck))‖=‖ημkρ(ck)‖≤η‖zk−ck‖. |
The global convergence result for Algorithm 1 is established via the following theorem.
Theorem 3.6. Suppose Assumption 1-3 is satisfied and the sequences {zk} are generated by the Algorithm 1. Then we
lim infk→∞‖ρ(zk)‖=0. | (3.14) |
Proof. Suppose (3.14) does not hold, meaning there exist a constant ε0>0 such that
‖ρ(zk)‖≥ε0k≥0. | (3.15) |
By (2.8), we know
‖ρ(zk)‖‖jk‖≥−ρ(zk)Tjk≥α‖ρ(zk)‖2, |
which implies
‖jk‖≥α‖ρ(zk)‖≥ε0,∀k≥0. | (3.16) |
By (2.3), we have
‖jk‖=‖−πkρ(zk)+βkwk−1‖=‖−(c+βkρ(zk)Twk−1‖ρ(zk−1)‖2)ρ(zk)+((1−θk)ρ(zk)Tyk−1−ρ(zk−1)Tjk−1+θk‖ρ(zk)‖2‖ρ(zk−1)‖2)wk−1‖≤l‖ρ(zk)‖+|βk|‖wk−1‖+(‖ρ(zk)‖|ρ(zk−1)Tjk−1|‖yk−1‖+‖ρ(zk)‖2‖ρ(zk−1)‖2)‖wk−1‖≤l‖ρ(zk)‖+2(‖ρ(zk)‖|ρ(zk−1)Tjk−1|‖yk−1‖+‖ρ(zk)‖2‖ρ(zk−1)‖2)‖wk−1‖≤l‖ρ(zk)‖+2(‖ρ(zk)‖α‖ρ(zk−1)‖2tk−1‖jk−1‖+‖ρ(zk)‖2‖ρ(zk−1)‖2)tk−1‖jk−1‖≤lδ+2δε20(tk−1‖jk−1‖)2+2δ2ε20tk−1‖jk−1‖ |
for all k∈N. Since (3.13) holds, it follows that for every ε1>0 there exist k0 such that tk−1‖jk−1‖<ε1 for every k>k0. Choosing ε1=ε0 and ℓ0=max{‖j0‖,‖j1‖,⋯,‖jk0‖,ℓ01} where ℓ01=δ(c+2+2δ/ε0), it holds that
‖jk‖≤ℓ0 | (3.17) |
for every k∈N. Integrating with (3.4),(3.15),(3.16) and (3.17), we know that for any k sufficiently large
tk‖jk‖≥min{1,τ(L+κ)‖ρ(zk)‖2‖jk‖2}‖jk‖=min{‖jk‖,τ(L+κ)‖ρ(zk)‖2‖jk‖}≥min{ε0,τε20(L+κ)ℓ0} |
The last inequality yields a contradiction with (b) in Lemma 3.5. Consequently, (3.14) holds. The proof is completed.
The Dolan and Moré performance profile [29] is used in this section to evaluate the efficiency of the proposed algorithm on a set of test problems with varying dimensions and initial points. Comparison is made with algorithm of the same class proposed in [30]. All codes were written in MATLAB environment and compiled on a HP laptop (CPU Corei3-2.5 GHz, RAM 8 GB) with Windows 10 operating system.
● Algo.1: The new method (Algorithm 1).
● Algo.2: MFRM method proposed in [30].
The parameters for Algo.1 are chosen as: τ=0.9,κ=10−4,η=1.2. While parameters for Algo.2 are set as reported in [30]. All iterative procedure are terminated whenever ‖ρ(zk)‖<10−6. The experiment is carried out on nine different problems with dimensions ranging from n=1000,5000,10,000,50,000,100,000 using seven different initial points: z1=(0.1,⋯,0.1)T,z2=(0.2,⋯,0.2)T,z3=(0.5,⋯,0.5)T,z4=(1.2,⋯,1.2)T,z5=(1.5,⋯,1.5)T,z6=(2,⋯,2)T and z7=rand(n,1). The test problems considered are listed the below where the mapping ρ(z)=(ρ1(z),ρ2(z),⋯,ρn(z))T
Problem 1 [31] Exponential Function.
ρ1(z)=ez1−1,ρi(z)=ezi+zi−1,for i=2,3,...,n,and Ω=Rn+. |
Problem 2 [31] Modified Logarithmic Function.
ρi(z)=ln(zi+1)−zin,for i=1,2,3,...,n,and Ω={z∈Rn:n∑i=1zi≤n,zi>−1,i=1,2,⋯,n}. |
Problem 3 [32]
ρi(z)=min(min(|zi|,z2i),max(|zi|,z3i))for i=2,3,...,n,and Ω=Rn+. |
Problem 4 [31] Strictly Convex Function I.
ρi(z)=ezi−1,for i=1,2,...,n,and Ω=Rn+. |
Problem 5 [31] Strictly Convex Function II.
ρi(z)=inezi−1,for i=1,2,...,n,and Ω=Rn+. |
Problem 6 [33] Tridiagonal Exponential Function.
ρ1(z)=z1−ecos(h(z1+z2)),ρi(z)=zi−ecos(h(zi−1+zi+zi+1)),for i=2,...,n−1,ρn(z)=zn−ecos(h(zn−1+zn)),h=1n+1 |
Problem 7 [34] Nonsmooth Function.
ρi(z)=zi−sin|zi−1|,i=1,2,3,...,n,and Ω={z∈Rn:n∑i=1zi≤n,zi≥−1,i=1,2,⋯,n}. |
Problem 8 [31] The Trig exp function
ρ1(z)=3z31+2z2−5+sin(z1−z2)sin(z1+z2)ρi(z)=3z3i+2zi+1−5+sin(zi−zi+1)sin(zi+zi+1)+4zi−zi−1ezi−1−zi−3fori=2,3,...,n−1ρn(z)=zn−1ezn−1−zn−4zn−3,where h=1m+1 and Ω=Rn+.. |
Problem 9 [35]
ti=n∑i=1z2i,c=10−5ρi(z)=2c(zi−1)+4(ti−0.25)zi,i=1,2,3,...,n.and Ω=Rn+. |
Figures 1-3 presents the results of the comparisons of the mentioned methods. Figure 1 shows the graph of the two methods where the performance measure is the total number of iterations. In the figure, we see that the Algo.1 obtain the most wins with the probability around 78 % and the Algo.2 method is in the second place. Figure 2 shows the performance of the considered methods relative to the total number of function evaluation. Graph of this measure shows that Algo.1 has better performance in comparison with Algo.2. In Figure 3 the performance measure is the CPU running time. The CPU running time figure also indicates that Algo.1 outperforms Algo.2. From the presented figures, it is clear that Algo.1 is the most efficient in solving the considered test problems. A detailed result of the numerical experiment for the test problems is reported in Table 2-10 in the appendix section.
The restoration of images is a process in which a distorted or damaged image is restored to its original form. Having an algorithm that can perform such function with high restoration efficiency is of importance. We consider the signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) as a metric for measuring the restoration efficiency. SNR, PSNR and SSIM's larger values reflect better quality of the restored images and indicate that the restored images are closer to the original. Consider the following disturbed or incomplete observation
b=ρz+ω, | (5.1) |
where z∈Rn,b∈Rk is the observation data, ρ∈Rk×n(k<<n) is a linear operator and ω∈Rk is an error term. Our goal in this section is to recover the unknown vector z. A well-known approach for obtaining z is by solving the following ℓ1-regularization problem
minz∈Rn{σ‖z‖1+12‖ρz−b‖22} | (5.2) |
where the regularization term σ is positive, ‖⋅‖1, and ‖⋅‖2 are the ℓ1-norm and ℓ2-norm respectively. See (Refs. [36,37,38,39,40]) for various algorithms for solving (5.2). For a comprehensive procedure on how to use our proposed algorithm to solve (5.2), see [41,42].
To assess the efficiency of Algo.1 in restoring the images degraded using a Gaussian blur kernel of standard deviation 0.1, we compare its performance with the modified Fletcher-Reeves conjugate Gradient method proposed in [30]. The algorithm is referred to as Algo.2. Four test images with different sizes are considered in this experiment. The images are labelled as A, B, C and D. The algorithms are implemented based on the following
● All codes were written and implemented in Matlab environment.
● Same starting point and stopping condition (with Tol=10−5) for all the algorithms.
● Parameters for Algo.1, are chosen as η=1,τ=0.55,κ=10−4. Parameters for Algo.2 are chosen as reported in the application section of [30].
● The linear operator ρ in the experiment is choosen as the Gaussian matrix generated by the command rand(k,n) in MATLAB.
● The signal-to-noise ratio (SNR) is defined as
SNR:=20×log10(‖z‖‖˜z−z‖), |
where ˜z is recovered vector. The definition of the peak-to-signal and the structural similarity index (SSIM) ratio (PSNR) can be found in [43] and [44], respectively.
Algo.1 | Algo.2 | |||||
Test Image | SNR | PSNR | SSIM | SNR | PSNR | SSIM |
A | 16.74 | 19.03 | 0.765 | 16.66 | 18.95 | 0.760 |
B | 16.65 | 21.98 | 0.911 | 16.59 | 21.93 | 0.910 |
C | 20.93 | 22.76 | 0.913 | 20.87 | 22.70 | 0.912 |
D | 18.80 | 21.71 | 0.931 | 18.68 | 21.58 | 0.929 |
Figure 4 has four columns labelled ORI, BNI, RA1 and RA2. Images on the column labelled ORI are the original images, images on the column labelled BNI are the blurred and noisy images. RA1 are the images restored by Algo.1 and RA2 are images restored by Algo.2. Table 1 provides the SNR, PSNR and SSIM values for Algo.1 and Algo.2. It can be seen that Algo.1 has the highest SNR, PSNR and SSIM in all the images used for the experiment. This indicates that Algo.1 is more effective than Algo.2 in restoring blurred and noisy images.
"The authors acknowledge the support provided by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart research Innovation Cluster (CLASSIC), Faculty of Science, KMUTT. The first author was supported by the Petchra Pra Jom Klao Doctoral Scholarship, Academic for Ph.D. Program at KMUTT (Grant No.16/2561)."
The authors declare that they have no conflict of interest.
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 3 | 11 | 0.020026 | 0 | 32 | 128 | 0.15285 | 5.77E-07 |
z2 | 2 | 7 | 0.022233 | 0 | 23 | 92 | 0.046757 | 1.03E-07 | |
z3 | 3 | 11 | 0.028924 | 0.00E+00 | 43 | 172 | 0.085067 | 3.24E-07 | |
z4 | 2 | 7 | 0.01272 | 0.00E+00 | 28 | 112 | 0.042162 | 8.50E-07 | |
z5 | 2 | 7 | 0.012594 | 0 | 38 | 152 | 0.082875 | 7.44E-07 | |
z6 | 2 | 7 | 0.006795 | 0.00E+00 | 34 | 136 | 0.061034 | 4.36E-07 | |
z7 | 29 | 116 | 0.098046 | 3.71E-08 | 62 | 248 | 0.1162 | 3.84E-07 | |
5000 | z1 | 2 | 7 | 0.1681 | 0 | 16 | 64 | 0.097823 | 4.98E-07 |
z2 | 2 | 7 | 0.07673 | 0 | 27 | 108 | 0.16998 | 5.89E-08 | |
z3 | 2 | 7 | 0.019262 | 0.00E+00 | 34 | 136 | 0.43167 | 8.96E-07 | |
z4 | 2 | 7 | 0.041163 | 0.00E+00 | 43 | 172 | 0.24401 | 4.77E-07 | |
z5 | 2 | 7 | 0.035437 | 0.00E+00 | 36 | 144 | 0.28409 | 4.72E-07 | |
z6 | 2 | 7 | 0.031377 | 0 | 25 | 100 | 0.1577 | 8.50E-07 | |
z7 | 68 | 272 | 1.5225 | 2.22E-08 | NaN | NaN | NaN | NaN | |
10000 | z1 | 2 | 7 | 0.067548 | 0 | 7 | 28 | 0.080462 | 7.04E-07 |
z2 | 2 | 7 | 0.02502 | 0 | 24 | 96 | 0.9236 | 2.84E-07 | |
z3 | 2 | 7 | 0.037267 | 0.00E+00 | 21 | 84 | 0.82591 | 6.94E-07 | |
z4 | 2 | 7 | 0.027143 | 0 | 38 | 152 | 0.97602 | 5.16E-07 | |
z5 | 2 | 7 | 0.070627 | 0 | 28 | 112 | 0.46927 | 8.68E-07 | |
z6 | 2 | 7 | 0.052355 | 0 | 25 | 100 | 0.28425 | 8.52E-07 | |
z7 | 107 | 428 | 9.536 | 3.42E-08 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.35904 | 0 | 7 | 28 | 0.29707 | 2.32E-07 |
z2 | 2 | 7 | 0.24819 | 0 | 15 | 60 | 1.212 | 2.10E-07 | |
z3 | 2 | 7 | 0.21212 | 0.00E+00 | 7 | 28 | 0.33872 | 7.76E-07 | |
z4 | 2 | 7 | 0.265 | 0.00E+00 | 24 | 96 | 1.2315 | 7.36E-07 | |
z5 | 2 | 7 | 0.22679 | 0.00E+00 | 21 | 84 | 0.98662 | 9.19E-07 | |
z6 | 2 | 7 | 0.46048 | 0.00E+00 | 8 | 32 | 0.44742 | 4.62E-07 | |
z7 | 353 | 1412 | 85.8011 | 1.12E-11 | NaN | NaN | NaN | NaN | |
100000 | z1 | 2 | 7 | 0.26127 | 0 | 7 | 28 | 0.66487 | 2.45E-07 |
z2 | 2 | 7 | 0.42916 | 0 | 14 | 56 | 1.9555 | 4.72E-07 | |
z3 | 2 | 7 | 0.29924 | 0.00E+00 | 7 | 28 | 0.65463 | 8.36E-07 | |
z4 | 2 | 7 | 0.47753 | 0 | 28 | 112 | 4.5812 | 5.94E-07 | |
z5 | 2 | 7 | 0.28228 | 0.00E+00 | 17 | 68 | 2.0596 | 5.23E-07 | |
z6 | 2 | 7 | 0.45284 | 0.00E+00 | 8 | 32 | 1.4187 | 3.26E-07 | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 7 | 22 | 0.047242 | 1.58E-09 | 4 | 12 | 0.075993 | 5.17E-07 |
z2 | 7 | 22 | 0.011612 | 2.12E-09 | 5 | 15 | 0.01685 | 6.04E-09 | |
z3 | 6 | 19 | 0.008748 | 7.52E-09 | 5 | 15 | 0.009081 | 4.37E-07 | |
z4 | 8 | 25 | 0.008643 | 1.95E-09 | 6 | 18 | 0.009114 | 1.52E-07 | |
z5 | 6 | 19 | 0.010119 | 8.43E-09 | 7 | 21 | 0.013185 | 1.10E-09 | |
z6 | 9 | 28 | 0.009592 | 1.04E-09 | 7 | 21 | 0.014685 | 1.74E-08 | |
z7 | 44 | 169 | 0.043234 | 9.47E-07 | 69 | 261 | 0.22456 | 6.30E-07 | |
5000 | z1 | 6 | 20 | 0.062266 | 2.97E-07 | 4 | 12 | 0.012773 | 1.75E-07 |
z2 | 6 | 20 | 0.031005 | 4.05E-07 | 5 | 15 | 0.019072 | 6.27E-10 | |
z3 | 6 | 19 | 0.022469 | 9.12E-10 | 5 | 15 | 0.03412 | 1.42E-07 | |
z4 | 7 | 23 | 0.048441 | 3.74E-07 | 6 | 18 | 0.040398 | 3.94E-08 | |
z5 | 6 | 19 | 0.032782 | 1.42E-09 | 6 | 18 | 0.030696 | 4.05E-07 | |
z6 | 7 | 22 | 0.038421 | 7.12E-09 | 7 | 21 | 0.02232 | 2.36E-09 | |
z7 | 45 | 169 | 0.32315 | 1.74E-07 | 75 | 290 | 0.68505 | 9.20E-07 | |
10000 | z1 | 5 | 16 | 0.065175 | 9.23E-09 | 4 | 12 | 0.05281 | 1.21E-07 |
z2 | 6 | 21 | 0.072794 | 3.06E-07 | 5 | 15 | 0.055137 | 2.79E-10 | |
z3 | 6 | 19 | 0.036537 | 4.32E-10 | 5 | 15 | 0.038347 | 9.73E-08 | |
z4 | 7 | 24 | 0.054625 | 2.82E-07 | 6 | 18 | 0.057504 | 2.56E-08 | |
z5 | 6 | 20 | 0.09281 | 7.38E-10 | 6 | 18 | 0.053546 | 2.93E-07 | |
z6 | 7 | 22 | 0.098951 | 4.21E-09 | 7 | 21 | 0.05207 | 1.24E-09 | |
z7 | 34 | 133 | 0.35652 | 8.45E-07 | 75 | 286 | 1.1715 | 8.81E-07 | |
50000 | z1 | 7 | 26 | 1.0892 | 1.84E-07 | 4 | 12 | 0.072347 | 6.32E-08 |
z2 | 9 | 34 | 0.57121 | 3.87E-07 | 5 | 16 | 0.17135 | 6.75E-11 | |
z3 | 6 | 21 | 0.17777 | 5.88E-07 | 5 | 15 | 0.30908 | 4.87E-08 | |
z4 | 10 | 37 | 0.79714 | 3.60E-07 | 6 | 18 | 0.30538 | 1.11E-08 | |
z5 | 7 | 25 | 0.14544 | 1.16E-07 | 6 | 18 | 0.17986 | 1.84E-07 | |
z6 | 8 | 28 | 0.24313 | 7.93E-07 | 7 | 21 | 0.11731 | 4.01E-10 | |
z7 | 36 | 141 | 1.1389 | 1.07E-07 | 87 | 326 | 3.3093 | 3.83E-07 | |
100000 | z1 | 7 | 26 | 0.35609 | 2.56E-07 | 4 | 12 | 0.23409 | 5.40E-08 |
z2 | 9 | 34 | 0.43666 | 5.47E-07 | 5 | 16 | 0.3152 | 4.27E-11 | |
z3 | 6 | 21 | 0.31721 | 7.65E-07 | 5 | 15 | 0.28597 | 4.05E-08 | |
z4 | 10 | 37 | 0.53074 | 5.09E-07 | 6 | 18 | 0.23003 | 8.15E-09 | |
z5 | 7 | 25 | 0.27827 | 1.55E-07 | 6 | 18 | 0.45582 | 1.80E-07 | |
z6 | 9 | 32 | 0.5333 | 1.09E-07 | 7 | 22 | 0.2709 | 2.71E-10 | |
z7 | 31 | 121 | 1.7511 | 5.10E-07 | 81 | 306 | 6.1345 | 9.16E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 6 | 0.007199 | 0 | 2 | 6 | 0.026849 | 0 |
z2 | 2 | 6 | 0.00552 | 0 | 2 | 6 | 0.003173 | 0 | |
z3 | 2 | 6 | 0.006377 | 0 | 2 | 6 | 0.006714 | 0 | |
z4 | 3 | 11 | 0.017561 | 0.00E+00 | 2 | 6 | 0.005403 | 0 | |
z5 | 3 | 11 | 0.007556 | 0.00E+00 | 2 | 6 | 0.009761 | 0 | |
z6 | 3 | 11 | 0.008376 | 0 | 2 | 6 | 0.003285 | 0 | |
z7 | 16 | 49 | 0.043387 | 2.91E-07 | 2 | 6 | 0.005238 | 0 | |
5000 | z1 | 2 | 6 | 0.024798 | 0 | 2 | 6 | 0.037672 | 0 |
z2 | 2 | 6 | 0.017882 | 0 | 2 | 6 | 0.016857 | 0 | |
z3 | 2 | 6 | 0.014761 | 0 | 2 | 6 | 0.016971 | 0 | |
z4 | 3 | 11 | 0.021926 | 0.00E+00 | 2 | 6 | 0.024599 | 0 | |
z5 | 3 | 11 | 0.019501 | 0.00E+00 | 2 | 6 | 0.12878 | 0 | |
z6 | 3 | 11 | 0.099645 | 0 | 2 | 6 | 0.016172 | 0 | |
z7 | 21 | 65 | 0.26663 | 8.91E-07 | 2 | 6 | 0.068901 | 0 | |
10000 | z1 | 2 | 6 | 0.053329 | 0 | 2 | 6 | 0.039629 | 0 |
z2 | 2 | 6 | 0.036889 | 0 | 2 | 6 | 0.029941 | 0 | |
z3 | 2 | 6 | 0.02419 | 0 | 2 | 6 | 0.022097 | 0 | |
z4 | 3 | 11 | 0.046062 | 0.00E+00 | 2 | 6 | 0.015668 | 0 | |
z5 | 3 | 11 | 0.17699 | 0.00E+00 | 2 | 6 | 0.1442 | 0 | |
z6 | 3 | 11 | 0.056058 | 0 | 2 | 6 | 0.080865 | 0 | |
z7 | 19 | 58 | 0.42057 | 1.22E-07 | 2 | 6 | 0.052839 | 0 | |
50000 | z1 | 2 | 6 | 0.11901 | 0 | 2 | 6 | 0.27419 | 0 |
z2 | 2 | 6 | 0.10804 | 0 | 2 | 6 | 0.228 | 0 | |
z3 | 2 | 6 | 0.15799 | 0 | 2 | 6 | 0.083129 | 0 | |
z4 | 3 | 11 | 0.27797 | 0.00E+00 | 2 | 6 | 0.09131 | 0 | |
z5 | 3 | 11 | 0.21594 | 0.00E+00 | 2 | 6 | 0.047357 | 0 | |
z6 | 3 | 11 | 0.16137 | 0 | 2 | 6 | 0.049002 | 0 | |
z7 | 21 | 64 | 1.156 | 3.21E-07 | 2 | 6 | 0.12806 | 0 | |
100000 | z1 | 2 | 6 | 0.21976 | 0 | 2 | 6 | 0.15418 | 0 |
z2 | 2 | 6 | 0.19397 | 0 | 2 | 6 | 0.44568 | 0 | |
z3 | 2 | 6 | 0.17969 | 0 | 2 | 6 | 0.79033 | 0 | |
z4 | 3 | 11 | 0.30701 | 0.00E+00 | 2 | 6 | 0.20222 | 0 | |
z5 | 3 | 11 | 0.72994 | 0.00E+00 | 2 | 6 | 0.20959 | 0 | |
z6 | 3 | 11 | 0.36806 | 0 | 2 | 6 | 0.26684 | 0 | |
z7 | 22 | 67 | 1.8809 | 2.86E-07 | 2 | 6 | 0.23472 | 0 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 7 | 0.007686 | 0 | 8 | 31 | 0.025113 | 1.65E-07 |
z2 | 2 | 7 | 0.004973 | 0 | 7 | 28 | 0.007628 | 2.32E-07 | |
z3 | 2 | 7 | 0.004693 | 0.00E+00 | 8 | 32 | 0.009827 | 7.42E-07 | |
z4 | 2 | 7 | 0.005652 | 0.00E+00 | 9 | 35 | 0.012267 | 1.62E-07 | |
z5 | 2 | 7 | 0.007206 | 0.00E+00 | 7 | 28 | 0.012782 | 3.92E-07 | |
z6 | 2 | 7 | 0.005871 | 0.00E+00 | 8 | 32 | 0.016455 | 3.68E-07 | |
z7 | 22 | 87 | 0.030189 | 0.00E+00 | 71 | 284 | 0.045157 | 1.91E-07 | |
5000 | z1 | 2 | 7 | 0.01789 | 0 | 8 | 31 | 0.035804 | 3.68E-07 |
z2 | 2 | 7 | 0.083644 | 0 | 7 | 28 | 0.056219 | 5.20E-07 | |
z3 | 2 | 7 | 0.019787 | 0.00E+00 | 9 | 36 | 0.028182 | 1.66E-07 | |
z4 | 2 | 7 | 0.02077 | 0 | 9 | 35 | 0.028652 | 3.61E-07 | |
z5 | 2 | 7 | 0.023139 | 0 | 7 | 28 | 0.09901 | 8.76E-07 | |
z6 | 2 | 7 | 0.045152 | 0 | 8 | 32 | 0.046074 | 8.22E-07 | |
z7 | 77 | 308 | 0.88375 | 2.85E-07 | 51 | 204 | 0.12808 | 9.55E-07 | |
10000 | z1 | 2 | 7 | 0.025792 | 0 | 8 | 32 | 0.043945 | 5.20E-07 |
z2 | 2 | 7 | 0.020051 | 0 | 7 | 27 | 0.050306 | 7.35E-07 | |
z3 | 2 | 7 | 0.025936 | 0.00E+00 | 9 | 36 | 0.039643 | 2.35E-07 | |
z4 | 2 | 7 | 0.03822 | 0 | 9 | 35 | 0.041378 | 5.11E-07 | |
z5 | 2 | 7 | 0.03849 | 0 | 8 | 32 | 0.13231 | 1.24E-07 | |
z6 | 2 | 7 | 0.031354 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z7 | 101 | 404 | 3.4918 | 4.06E-09 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.091176 | 0 | 9 | 34 | 0.23565 | 0 |
z2 | 2 | 7 | 0.090561 | 0 | NaN | NaN | NaN | NaN | |
z3 | 2 | 7 | 0.13857 | 0.00E+00 | 9 | 35 | 0.12604 | 5.25E-07 | |
z4 | 2 | 7 | 0.10731 | 0.00E+00 | 10 | 38 | 0.426 | 0 | |
z5 | 2 | 7 | 0.14284 | 0.00E+00 | 8 | 31 | 0.47179 | 2.77E-07 | |
z6 | 2 | 7 | 0.29418 | 0.00E+00 | 9 | 35 | 0.21126 | 2.60E-07 | |
z7 | 110 | 439 | 8.6871 | 0 | 44 | 176 | 1.2526 | 3.55E-07 | |
100000 | z1 | 2 | 7 | 0.20371 | 0 | 9 | 36 | 0.2659 | 1.65E-07 |
z2 | 2 | 7 | 0.26727 | 0 | 8 | 30 | 0.48604 | 0 | |
z3 | 2 | 7 | 0.1588 | 0.00E+00 | 9 | 35 | 0.35032 | 7.42E-07 | |
z4 | 2 | 7 | 0.20624 | 0.00E+00 | 10 | 39 | 0.34301 | 1.62E-07 | |
z5 | 2 | 7 | 0.19404 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z6 | 2 | 7 | 0.21718 | 0.00E+00 | 9 | 35 | 0.31142 | 3.68E-07 | |
z7 | 111 | 444 | 18.0039 | 6.11E-08 | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 34 | 127 | 0.026467 | 1.62E-07 | 71 | 263 | 0.16103 | 3.21E-07 |
z2 | 36 | 140 | 0.026972 | 7.43E-07 | 62 | 235 | 0.052281 | 1.13E-07 | |
z3 | 52 | 205 | 0.16096 | 2.58E-07 | 50 | 194 | 0.088863 | 3.72E-07 | |
z4 | 96 | 378 | 0.55079 | 4.35E-07 | NaN | NaN | NaN | NaN | |
z5 | 123 | 492 | 0.48012 | 3.96E-07 | NaN | NaN | NaN | NaN | |
z6 | 196 | 784 | 1.0967 | 6.21E-07 | NaN | NaN | NaN | NaN | |
z7 | 115 | 459 | 0.34961 | 2.89E-07 | NaN | NaN | NaN | NaN | |
5000 | z1 | 59 | 232 | 0.68163 | 2.32E-07 | 63 | 231 | 0.30231 | 3.90E-07 |
z2 | 50 | 188 | 0.29441 | 6.42E-07 | 72 | 282 | 0.18091 | 7.31E-07 | |
z3 | 179 | 709 | 2.2218 | 2.91E-07 | 60 | 232 | 0.14861 | 1.47E-07 | |
z4 | 171 | 684 | 2.9204 | 2.99E-07 | NaN | NaN | NaN | NaN | |
z5 | 297 | 1187 | 5.9983 | 3.31E-07 | NaN | NaN | NaN | NaN | |
z6 | 420 | 1680 | 9.6236 | 1.67E-07 | NaN | NaN | NaN | NaN | |
z7 | 187 | 744 | 3.4767 | 8.43E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 300 | 1.3784 | 1.39E-07 | 75 | 283 | 0.27114 | 2.35E-07 |
z2 | 74 | 283 | 1.5399 | 1.34E-07 | 55 | 208 | 0.20873 | 3.12E-07 | |
z3 | 214 | 843 | 5.0625 | 9.68E-07 | 67 | 259 | 0.65684 | 2.52E-07 | |
z4 | 253 | 1012 | 8.4598 | 5.48E-07 | NaN | NaN | NaN | NaN | |
z5 | 383 | 1531 | 15.2491 | 1.45E-07 | NaN | NaN | NaN | NaN | |
z6 | 575 | 2300 | 24.956 | 4.27E-07 | NaN | NaN | NaN | NaN | |
z7 | 323 | 1291 | 9.6152 | 2.90E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 135 | 534 | 12.3192 | 9.85E-07 | 65 | 253 | 1.9331 | 1.74E-07 |
z2 | 342 | 1357 | 46.7469 | 1.53E-07 | 94 | 369 | 4.3154 | 4.77E-07 | |
z3 | 326 | 1294 | 39.8986 | 4.97E-07 | NaN | NaN | NaN | NaN | |
z4 | 504 | 2016 | 82.9841 | 3.45E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | 602 | 2403 | 97.0953 | 6.65E-07 | NaN | NaN | NaN | NaN | |
100000 | z1 | 164 | 645 | 25.8558 | 1.87E-07 | NaN | NaN | NaN | NaN |
z2 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z3 | 400 | 1590 | 126.0758 | 7.38E-07 | NaN | NaN | NaN | NaN | |
z4 | 636 | 2544 | 240.5206 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 9 | 36 | 0.17935 | 8.25E-07 | 9 | 36 | 0.0153 | 8.24E-07 |
z2 | 9 | 36 | 0.03051 | 7.93E-07 | 9 | 36 | 0.048509 | 7.93E-07 | |
z3 | 9 | 36 | 0.027967 | 6.99E-07 | 9 | 36 | 0.017521 | 6.98E-07 | |
z4 | 9 | 36 | 0.015472 | 4.79E-07 | 9 | 36 | 0.014811 | 4.78E-07 | |
z5 | 9 | 36 | 0.007122 | 3.84E-07 | 9 | 36 | 0.016431 | 3.83E-07 | |
z6 | 9 | 36 | 0.010164 | 2.27E-07 | 9 | 36 | 0.009737 | 2.26E-07 | |
z7 | 9 | 36 | 0.020191 | 7.23E-07 | 9 | 36 | 0.017515 | 7.06E-07 | |
5000 | z1 | 10 | 40 | 0.048118 | 1.85E-07 | 10 | 40 | 0.082844 | 1.85E-07 |
z2 | 10 | 40 | 0.097072 | 1.78E-07 | 10 | 40 | 0.050343 | 1.78E-07 | |
z3 | 10 | 40 | 0.032297 | 1.57E-07 | 10 | 40 | 0.10792 | 1.57E-07 | |
z4 | 10 | 40 | 0.043942 | 1.07E-07 | 10 | 40 | 0.076199 | 1.07E-07 | |
z5 | 9 | 36 | 0.043841 | 8.61E-07 | 9 | 36 | 0.037916 | 8.61E-07 | |
z6 | 9 | 36 | 0.033263 | 5.08E-07 | 9 | 36 | 0.069375 | 5.08E-07 | |
z7 | 10 | 40 | 0.037194 | 1.58E-07 | 10 | 40 | 0.047672 | 1.58E-07 | |
10000 | z1 | 10 | 40 | 0.082406 | 2.62E-07 | 10 | 40 | 0.076648 | 2.62E-07 |
z2 | 10 | 40 | 0.068947 | 2.52E-07 | 10 | 40 | 0.15678 | 2.52E-07 | |
z3 | 10 | 40 | 0.058721 | 2.22E-07 | 10 | 40 | 0.13597 | 2.22E-07 | |
z4 | 10 | 40 | 0.078257 | 1.52E-07 | 10 | 40 | 0.08399 | 1.52E-07 | |
z5 | 10 | 40 | 0.062069 | 1.22E-07 | 10 | 40 | 0.07822 | 1.22E-07 | |
z6 | 9 | 36 | 0.053275 | 7.18E-07 | 9 | 36 | 0.1205 | 7.18E-07 | |
z7 | 10 | 40 | 0.057688 | 2.24E-07 | 10 | 40 | 0.080168 | 2.23E-07 | |
50000 | z1 | 10 | 40 | 0.22352 | 5.85E-07 | 10 | 39 | 0.38243 | 5.85E-07 |
z2 | 10 | 40 | 0.27436 | 5.63E-07 | 10 | 39 | 0.41361 | 5.63E-07 | |
z3 | 10 | 40 | 0.23122 | 4.96E-07 | 10 | 39 | 0.30721 | 4.96E-07 | |
z4 | 10 | 40 | 0.21192 | 3.40E-07 | 10 | 39 | 0.43086 | 3.40E-07 | |
z5 | 10 | 40 | 0.23892 | 2.72E-07 | 10 | 38 | 0.29829 | 1.26E-15 | |
z6 | 10 | 40 | 0.29017 | 1.61E-07 | 10 | 38 | 0.51415 | 6.28E-16 | |
z7 | 10 | 40 | 0.25616 | 5.01E-07 | 10 | 39 | 0.29756 | 5.00E-07 | |
100000 | z1 | 10 | 40 | 0.82944 | 8.28E-07 | 10 | 39 | 1.1183 | 8.28E-07 |
z2 | 10 | 40 | 0.47168 | 7.96E-07 | 10 | 38 | 0.6117 | 6.28E-16 | |
z3 | 10 | 40 | 0.49749 | 7.01E-07 | 10 | 38 | 0.81145 | 6.28E-16 | |
z4 | 10 | 40 | 0.52125 | 4.80E-07 | 10 | 38 | 0.79886 | 0 | |
z5 | 10 | 40 | 0.69499 | 3.85E-07 | 10 | 38 | 0.60219 | 0 | |
z6 | 10 | 40 | 0.47656 | 2.27E-07 | 10 | 38 | 0.72864 | 0 | |
z7 | 10 | 40 | 0.49578 | 7.07E-07 | 10 | 39 | 0.80741 | 7.07E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 5 | 20 | 0.046544 | 3.24E-07 | 5 | 20 | 0.008647 | 3.24E-07 |
z2 | 5 | 20 | 0.009418 | 1.43E-07 | 5 | 20 | 0.013849 | 1.43E-07 | |
z3 | 5 | 20 | 0.038932 | 1.68E-08 | 4 | 16 | 0.015388 | 5.81E-08 | |
z4 | 6 | 24 | 0.01166 | 9.16E-09 | 6 | 24 | 0.010967 | 3.39E-08 | |
z5 | 6 | 24 | 0.010929 | 1.23E-08 | 6 | 24 | 0.0107 | 4.99E-08 | |
z6 | 6 | 23 | 0.01937 | 1.04E-07 | 6 | 23 | 0.014025 | 6.55E-08 | |
z7 | 26 | 104 | 0.032336 | 8.36E-09 | 36 | 144 | 0.12555 | 5.34E-08 | |
5000 | z1 | 5 | 20 | 0.029586 | 7.25E-07 | 5 | 20 | 0.041107 | 7.25E-07 |
z2 | 5 | 20 | 0.027892 | 3.20E-07 | 5 | 20 | 0.038182 | 3.20E-07 | |
z3 | 5 | 20 | 0.035333 | 3.75E-08 | 4 | 16 | 0.12123 | 1.30E-07 | |
z4 | 6 | 24 | 0.032225 | 2.05E-08 | 6 | 24 | 0.05211 | 7.58E-08 | |
z5 | 6 | 24 | 0.026546 | 2.75E-08 | 6 | 24 | 0.038675 | 1.12E-07 | |
z6 | 6 | 23 | 0.032529 | 2.32E-07 | 6 | 23 | 0.081384 | 1.46E-07 | |
z7 | 34 | 136 | 0.24122 | 3.59E-08 | 41 | 164 | 0.29917 | 1.14E-07 | |
10000 | z1 | 6 | 24 | 0.043879 | 5.12E-09 | 6 | 24 | 0.079589 | 5.12E-09 |
z2 | 5 | 20 | 0.036531 | 4.52E-07 | 5 | 20 | 0.1417 | 4.52E-07 | |
z3 | 5 | 20 | 0.050902 | 5.31E-08 | 4 | 16 | 0.045901 | 1.84E-07 | |
z4 | 6 | 24 | 0.054078 | 2.90E-08 | 6 | 24 | 0.059807 | 1.07E-07 | |
z5 | 6 | 24 | 0.052048 | 3.89E-08 | 6 | 24 | 0.099213 | 1.58E-07 | |
z6 | 6 | 23 | 0.04894 | 3.28E-07 | 6 | 23 | 0.054029 | 2.07E-07 | |
z7 | 41 | 164 | 0.30793 | 3.45E-08 | 45 | 180 | 0.92444 | 3.64E-07 | |
50000 | z1 | 6 | 24 | 0.14 | 1.15E-08 | 6 | 24 | 0.26027 | 1.15E-08 |
z2 | 6 | 24 | 0.14343 | 5.06E-09 | 6 | 24 | 0.60276 | 5.06E-09 | |
z3 | 5 | 20 | 0.15201 | 1.19E-07 | 4 | 16 | 0.17247 | 4.11E-07 | |
z4 | 6 | 24 | 0.34794 | 6.48E-08 | 6 | 24 | 0.22999 | 2.40E-07 | |
z5 | 6 | 24 | 0.15433 | 8.70E-08 | 6 | 24 | 0.38048 | 3.53E-07 | |
z6 | 6 | 23 | 0.1425 | 7.35E-07 | 6 | 23 | 0.2271 | 4.63E-07 | |
z7 | 29 | 116 | 1.295 | 9.41E-09 | 44 | 176 | 2.2436 | 7.06E-07 | |
100000 | z1 | 6 | 24 | 0.39791 | 1.62E-08 | 6 | 24 | 0.94834 | 1.62E-08 |
z2 | 6 | 24 | 0.47548 | 7.15E-09 | 6 | 24 | 0.43453 | 7.15E-09 | |
z3 | 5 | 20 | 0.48174 | 1.68E-07 | 4 | 16 | 0.29517 | 5.81E-07 | |
z4 | 6 | 24 | 0.26721 | 9.16E-08 | 6 | 24 | 0.55119 | 3.39E-07 | |
z5 | 6 | 24 | 0.28512 | 1.23E-07 | 6 | 24 | 0.61073 | 4.99E-07 | |
z6 | 7 | 27 | 0.5385 | 5.19E-09 | 6 | 23 | 0.42035 | 6.55E-07 | |
z7 | 29 | 116 | 1.6021 | 1.19E-08 | 41 | 164 | 3.9953 | 9.23E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 66 | 264 | 0.934 | 3.48E-07 | NaN | NaN | NaN | NaN |
z2 | 101 | 404 | 0.99428 | 4.28E-07 | 41 | 164 | 0.75214 | 4.29E-07 | |
z3 | 40 | 160 | 0.40127 | 3.33E-07 | NaN | NaN | NaN | NaN | |
z4 | 39 | 156 | 0.5071 | 5.07E-07 | 39 | 156 | 0.71207 | 3.83E-07 | |
z5 | 36 | 144 | 0.61923 | 4.69E-07 | 35 | 140 | 1.4123 | 4.07E-07 | |
z6 | 4 | 14 | 0.071864 | NaN | 4 | 14 | 0.059454 | NaN | |
z7 | 23 | 89 | 0.48051 | NaN | NaN | NaN | NaN | NaN | |
5000 | z1 | 52 | 208 | 2.7649 | 2.91E-07 | NaN | NaN | NaN | NaN |
z2 | 44 | 176 | 2.1027 | 3.54E-07 | NaN | NaN | NaN | NaN | |
z3 | 42 | 168 | 2.1325 | 2.95E-07 | NaN | NaN | NaN | NaN | |
z4 | 37 | 148 | 2.0738 | 3.41E-07 | NaN | NaN | NaN | NaN | |
z5 | 16 | 60 | 0.64982 | NaN | NaN | NaN | NaN | NaN | |
z6 | 20 | 76 | 0.98188 | NaN | NaN | NaN | NaN | NaN | |
z7 | 301 | 1202 | 18.7543 | 4.37E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 303 | 9.6495 | 3.64E-07 | NaN | NaN | NaN | NaN |
z2 | 71 | 284 | 8.0859 | 3.74E-07 | NaN | NaN | NaN | NaN | |
z3 | 62 | 248 | 7.1755 | 3.27E-07 | NaN | NaN | NaN | NaN | |
z4 | 48 | 192 | 4.1575 | 4.42E-07 | NaN | NaN | NaN | NaN | |
z5 | 15 | 55 | 0.93456 | NaN | NaN | NaN | NaN | NaN | |
z6 | 123 | 490 | 12.4072 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z7 | 307 | 1226 | 35.579 | 3.46E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 24 | 89 | 8.5017 | NaN | NaN | NaN | NaN | NaN |
z2 | 89 | 355 | 45.0395 | 4.34E-07 | NaN | NaN | NaN | NaN | |
z3 | 65 | 260 | 28.4752 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z4 | 431 | 1718 | 135.7493 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z5 | 6 | 21 | 2.1067 | NaN | NaN | NaN | NaN | NaN | |
z6 | 6 | 21 | 1.8349 | NaN | NaN | NaN | NaN | NaN | |
z7 | 7 | 24 | 1.8872 | NaN | NaN | NaN | NaN | NaN | |
100000 | z1 | 34 | 130 | 31.5135 | NaN | NaN | NaN | NaN | NaN |
z2 | 5 | 17 | 1.9076 | NaN | NaN | NaN | NaN | NaN | |
z3 | 87 | 332 | 64.5816 | 3.00E-07 | NaN | NaN | NaN | NaN | |
z4 | 76 | 303 | 68.3533 | 4.49E-07 | NaN | NaN | NaN | NaN | |
z5 | 5 | 17 | 2.2305 | NaN | NaN | NaN | NaN | NaN | |
z6 | 5 | 17 | 2.5293 | NaN | NaN | NaN | NaN | NaN | |
z7 | 6 | 21 | 3.1078 | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 10 | 34 | 0.032445 | 1.06E-07 | 10 | 34 | 0.005932 | 1.06E-07 |
z2 | 10 | 34 | 0.008239 | 1.06E-07 | 10 | 34 | 0.010335 | 1.06E-07 | |
z3 | 10 | 34 | 0.0073 | 1.06E-07 | 10 | 34 | 0.008407 | 1.06E-07 | |
z4 | 10 | 34 | 0.008495 | 1.06E-07 | 10 | 34 | 0.010614 | 1.06E-07 | |
z5 | 10 | 34 | 0.00772 | 1.06E-07 | 10 | 34 | 0.00775 | 1.06E-07 | |
z6 | 10 | 34 | 0.011383 | 1.06E-07 | 10 | 35 | 0.009311 | 1.06E-07 | |
z7 | 67 | 213 | 0.024778 | 9.71E-07 | 10 | 34 | 0.008864 | 1.06E-07 | |
5000 | z1 | 7 | 25 | 0.022534 | 6.89E-08 | 7 | 25 | 0.027033 | 6.89E-08 |
z2 | 7 | 25 | 0.032305 | 6.89E-08 | 7 | 25 | 0.02838 | 6.89E-08 | |
z3 | 7 | 25 | 0.026468 | 6.89E-08 | 7 | 25 | 0.068469 | 6.89E-08 | |
z4 | 7 | 25 | 0.034453 | 6.89E-08 | 7 | 26 | 0.037886 | 6.89E-08 | |
z5 | 7 | 25 | 0.021703 | 6.89E-08 | 7 | 26 | 0.037186 | 6.89E-08 | |
z6 | 7 | 25 | 0.027352 | 6.89E-08 | 7 | 26 | 0.077955 | 6.89E-08 | |
z7 | 20 | 66 | 0.061189 | 9.72E-07 | 7 | 25 | 0.037992 | 6.89E-08 | |
10000 | z1 | 6 | 22 | 0.07498 | 8.13E-08 | 6 | 22 | 0.054682 | 8.13E-08 |
z2 | 6 | 22 | 0.047478 | 8.13E-08 | 6 | 22 | 0.21797 | 8.13E-08 | |
z3 | 6 | 22 | 0.052347 | 8.13E-08 | 6 | 22 | 0.081579 | 8.13E-08 | |
z4 | 6 | 22 | 0.047644 | 8.13E-08 | 6 | 23 | 0.085064 | 8.13E-08 | |
z5 | 6 | 22 | 0.068304 | 8.13E-08 | 6 | 23 | 0.19028 | 8.13E-08 | |
z6 | 6 | 22 | 0.042771 | 8.13E-08 | 6 | 23 | 0.15365 | 8.13E-08 | |
z7 | 12 | 41 | 0.074071 | 9.08E-07 | 6 | 22 | 0.056989 | 8.13E-08 | |
50000 | z1 | 5 | 19 | 0.22112 | 1.41E-07 | 5 | 19 | 0.60662 | 1.41E-07 |
z2 | 5 | 19 | 0.21638 | 1.41E-07 | 5 | 19 | 0.33244 | 1.41E-07 | |
z3 | 5 | 19 | 0.22186 | 1.41E-07 | 5 | 20 | 0.8389 | 1.41E-07 | |
z4 | 5 | 19 | 0.37207 | 1.41E-07 | 5 | 20 | 0.63139 | 1.41E-07 | |
z5 | 5 | 19 | 0.36107 | 1.41E-07 | 5 | 20 | 1.046 | 1.41E-07 | |
z6 | 5 | 19 | 0.27063 | 1.41E-07 | 5 | 20 | 1.4673 | 1.41E-07 | |
z7 | 59 | 235 | 2.7862 | 4.11E-07 | 5 | 19 | 0.57234 | 1.41E-07 | |
100000 | z1 | 6 | 23 | 0.93893 | 2.10E-07 | 6 | 23 | 1.3525 | 2.10E-07 |
z2 | 6 | 23 | 0.60445 | 2.10E-07 | 6 | 24 | 1.5313 | 2.10E-07 | |
z3 | 6 | 23 | 0.71683 | 2.10E-07 | 6 | 24 | 1.6022 | 2.10E-07 | |
z4 | 6 | 23 | 0.57114 | 2.10E-07 | 6 | 24 | 1.7882 | 2.10E-07 | |
z5 | 6 | 23 | 0.57099 | 2.10E-07 | 6 | 24 | 1.878 | 2.10E-07 | |
z6 | 6 | 23 | 0.69104 | 2.10E-07 | 6 | 24 | 1.9634 | 2.10E-07 | |
z7 | 34 | 135 | 4.3899 | 4.52E-07 | 6 | 23 | 1.4688 | 2.10E-07 |
[1] |
Dizge N, Shaulsky E, Karanikola V (2019) Electrospun cellulose nanofibers for superhydrophobic and oleophobic membranes. J Membr Sci 590: 117271. doi: 10.1016/j.memsci.2019.117271
![]() |
[2] |
Pavlova ER, Bagrov DV, Monakhova KZ, et al. (2019) Tuning the properties of electrospun polylactide mats by ethanol treatment. Mater Des 181: 108061. doi: 10.1016/j.matdes.2019.108061
![]() |
[3] | Wang JN, Zhao WW, Wang B, et al. (2017) Multilevel-layer-structured polyamide 6/poly(trimethylene terephthalate) nanofibrous membranes for low-pressure air filtration. J Appl Pol Sci 134: 44716. |
[4] |
Cooper A, Oldinski R, Ma H Y, et al. (2013) Chitosan-based nanofibrous membranes for antibacterial filter applications. Carbohyd Polym 92: 254-259. doi: 10.1016/j.carbpol.2012.08.114
![]() |
[5] |
Banner J, Dautzenberg M, Feldhans T, et al. (2018) Water resistance and morphology of electrospun gelatine blended with citric acid and coconut oil. Tekstilec 61: 129-135. doi: 10.14502/Tekstilec2018.61.129-135
![]() |
[6] |
Grimmelsmann N, Homburg SV, Ehrmann A (2017) Electrospinning chitosan blends for nonwovens with morphologies between nanofiber mat and membrane. IOP Conf Series Mater Sci Eng 213: 012007. doi: 10.1088/1757-899X/213/1/012007
![]() |
[7] |
Wortmann M, Freese N, Sabantina L, et al. (2019) New polymers for needleless electrospinning from low-toxic solvents. Nanomater 9: 52. doi: 10.3390/nano9010052
![]() |
[8] |
Krasonu I, Tarassova E, Malmberg S, et al. (2019) Preparation of fibrous electrospun membranes with activated carbon filler. IOP Conf Series Mater Sci Eng 500: 012022. doi: 10.1088/1757-899X/500/1/012022
![]() |
[9] |
Plamus T, Savest N, Viirsalu M, et al. (2018) The effect of ionic liquids on the mechanical properties of electrospun polyacrylonitrile membranes. Polym Test 71: 335-343. doi: 10.1016/j.polymertesting.2018.09.003
![]() |
[10] |
Sabantina L, Mirasol JR, Cordero T, et al. (2018) Investigation of needleless electrospun PAN nanofiber mats. AIP Conf Proc 1952: 020085. doi: 10.1063/1.5032047
![]() |
[11] |
Wang JH, Cai C, Zhang ZJ, et al. (2020) Electrospun metal-organic frameworks with polyacrylonitrile as precursors to hierarchical porous carbon and composite nanofibers for adsorption and catalysis. Chemosphere 239: 124833. doi: 10.1016/j.chemosphere.2019.124833
![]() |
[12] |
de Oliveira JB, Guerrini LM, dos Santos Conejo L, et al. (2019) Viscoelastic evaluation of epoxy nanocomposite based on carbon nanofiber obtained from electrospinning processing. Polym Bull 76: 6063-6076. doi: 10.1007/s00289-019-02707-0
![]() |
[13] |
Trabelsi M, Mamun A, Klöcker M, et al. (2019) Increased mechanical properties of carbon nanofiber mats for possible medical applications. Fibers 7: 98. doi: 10.3390/fib7110098
![]() |
[14] |
Wang L, Zhang C, Gao F, et al. (2016) Needleless electrospinning for scaled-up production of ultrafine chitosan hybrid nanofibers used for air filtration. RSC Adv 6: 105988-105995. doi: 10.1039/C6RA24557A
![]() |
[15] |
Roche R, Yalcinkaya F (2018) Incorporation of PVDF nanofibre multilayers into functional structure for filtration applications. Nanomater 8: 771. doi: 10.3390/nano8100771
![]() |
[16] |
Lv D, Wang RX, Tang GS, et al. (2019) Ecofriendly electrospun membranes loaded with visible-light-responding nanoparticles for multifunctional usages: highly efficient air filtration, dye scavenging, and bactericidal activity. ACS Appl Mater Interfaces 11: 12880-12889. doi: 10.1021/acsami.9b01508
![]() |
[17] |
Fu QS, Lin G, Chen XD, et al. (2018) Mechanically reinforced PVdF/PMMA/SiO2 composite membrane and its electrochemical properties as a separator in lithium-ion batteries. Energy Technol 6: 144-152. doi: 10.1002/ente.201700347
![]() |
[18] |
Mamun A, Trabelsi M, Klöcker M, et al. (2019) Electrospun nanofiber mats with embedded non-sintered TiO2 for dye sensitized solar cells (DSSCs). Fibers 7: 60. doi: 10.3390/fib7070060
![]() |
[19] |
Xue YY, Guo X, Zhou HF, et al. (2019) Influence of beads-on-string on Na-Ion storage behavior in electrospun carbon nanofibers. Carbon 154: 219-229. doi: 10.1016/j.carbon.2019.08.003
![]() |
[20] |
Mamun A (2019) Review of possible applications of nanofibrous mats for wound dressings. Tekstilec 62: 89-100. doi: 10.14502/Tekstilec2019.62.89-100
![]() |
[21] |
Gao ST, Tang GS, Hua DW, et al. (2019) Stimuli-responsive bio-based polymeric systems and their applications. J Mater Chem B 7: 709-729. doi: 10.1039/C8TB02491J
![]() |
[22] |
Aljawish A, Muniglia L, Chevalot I (2016) Growth of human mesenchymal stem cells (MSCs) on films of enzymatically modified chitosan. Biotechnol Prog 32: 491-500. doi: 10.1002/btpr.2216
![]() |
[23] |
Muzzarelli RAA, EI Mehtedi M, Bottegoni C, et al. (2015) Genipin-crosslinked chitosan gels and scaffolds for tissue engineering and regeneration of cartilage and bone. Mar Drugs 13: 7314-7338. doi: 10.3390/md13127068
![]() |
[24] |
Klinkhammer K, Seiler N, Grafahrend D, et al. (2009) Deposition of electrospun fibers on reactive substrates for in vitro investigations. Tissue Eng Part C 15: 77-85. doi: 10.1089/ten.tec.2008.0324
![]() |
[25] |
Yoshida H, Klinkhammer K, Matsusaki M, et al. (2009) Disulfide-crosslinked electrospun poly(γ-glutamic acid) nonwovens as reduction-responsive scaffolds. Macromol Biosci 9: 568-574. doi: 10.1002/mabi.200800334
![]() |
[26] | Chatel A (2019) A brief history of adherent cell culture: where we come from and where we should go. BioProcess Int 17: 44-49. |
[27] | Whitford WG, Hardy JC, Cadwell JJS (2014) Single-use, continuous processing of primary stem cells. BioProcess Int 12: 26-32. |
[28] | Simon M (2015) Bioreactor design for adherent cell culture. The bolt-on bioreactor project, part 1: volumetric productivity. BioProcess Int 13: 28-33. |
[29] |
Allan SJ, De Bank PA, Ellis MJ (2019) Bioprocess design considerations for cultured meat production with a focus on the expansion bioreactor. Front Sus Food Syst 3: 44. doi: 10.3389/fsufs.2019.00044
![]() |
[30] | GE Healthcare Life Sciences (2013) Microcarrier Cell Culture, Principles and Methods.Available from: http://www.gelifesciences.co.kr/wp-content/uploads/2016/07/023.8_Microcarrier-Cell-Culture.pdf. |
[31] |
Lennaertz A, Knowles S, Drugmand JC, et al. (2013) Viral vector production in the integrity iCELLis single-use fixed-bed bioreactor, from bench-scale to industrial scale. BMC Proc 7: P59. doi: 10.1186/1753-6561-7-S6-P59
![]() |
[32] | Dohogne Y, Collignon F, Drugmand JC, et al. (2019) Scale-X bioreactor for viral vector production. Proof of concept for scalable HEK293 cell growth and adenovirus production, Univercell Application note.Available from: https://www.univercells.com/app/uploads/2019/05/scale-X%E2%84%A2-bioreactor-for-viral-production-Adeno_SFM.pdf. |
[33] |
Drugmand JC, Aghatos S, Schneider YJ, et al. (2007) Growth of mammalian and lepidopteram cells on BioNOC® II disks, a novel macroporous microcarrier. Cell Technology for Cell Products Heidelberg: Springer, 781-784. doi: 10.1007/978-1-4020-5476-1_143
![]() |
[34] |
Wehlage D, Blatter H, Sabantina L, et al. (2019) Sterilization of PAN/gelatin nanofibrous mats for cell growth. Tekstilec 62: 78-88. doi: 10.14502/Tekstilec2019.62.78-88
![]() |
[35] |
Ghasemi A, Imani R, Yousefzadeh M, et al. (2019) Studying the potential application of electrospun polyethylene terephthalate/graphene oxide nanofibers as electroconductive cardiac patc. Macromol Mater Eng 304: 1900187. doi: 10.1002/mame.201900187
![]() |
[36] |
Nekouian S, Sojoodi M, Nadri S (2019) Fabrication of conductive fibrous scaffold for photoreceptor differentiation of mesenchymal stem cell. J Cell Physiol 234: 15800-15808. doi: 10.1002/jcp.28238
![]() |
[37] |
Rahmani A, Nadri S, Kazemi HS, et al. (2019) Conductive electrospun scaffolds with electrical stimulation for neural differentiation of conjunctiva mesenchymal stem cells. Artif Organs 43: 780-790. doi: 10.1111/aor.13425
![]() |
[38] | Kutzli I, Beljo D, Gibis M, et al. (2019) Effect of maltodextrin dextrose equivalent on electrospinnability and glycation reaction of blends with pea protein isolate. Food Biophysics . |
[39] |
Diestelhorst E, Mance F, Mamun A, et al. (2020) Chemical and morphological modification of PAN nanofiber mats by addition of casein after electrospinning, stabilization and carbonization. Tekstilec 63: 38-49. doi: 10.14502/Tekstilec2020.63.38-49
![]() |
[40] |
Möller J, Korte K, Pörtner R, et al. (2018) Model-based identification of cell-cycle-dependent metabolism and putative autocrine effects in antibody producing CHO cell culture. Biotechnol Bioeng 115: 2996-3008. doi: 10.1002/bit.26828
![]() |
[41] |
Wippermann A, Rupp O, Brinkrolf K, et al. (2015) The DNA methylation landscape of Chinese hamster ovary (CHO) DP-12 cells. J Biotechnol 199: 38-46. doi: 10.1016/j.jbiotec.2015.02.014
![]() |
[42] |
Haredy AM, Nishizawa A, Honda K, et al. (2013) Improved antibody production in Chinese hamster ovary cells by ATF4 overexpression. Cytotechnology 65: 993-1002. doi: 10.1007/s10616-013-9631-x
![]() |
[43] |
Bazrafshan Z, Stylios GK (2018) Custom-built electrostatics and supplementary bonding in the design of reinforced Collagen-g-P (methyl methacrylate-co-ethyl acrylate)/nylon 66 core-shell fibers. J Mech Behav Biomed Mater 87: 19-29. doi: 10.1016/j.jmbbm.2018.07.002
![]() |
[44] |
Storck JL, Grothe T, Mamun A, et al. (2020) Orientation of electrospun magnetic nanofibers near conductive areas. Materials 13: 47. doi: 10.3390/ma13010047
![]() |
[45] |
Richter KN, Revelo NH, Seitz KJ, et al. (2018) Glyoxal as an alternative fixative to formaldehyde in immunostaining and super-resolution microscopy. EMBO J 37: 139-159. doi: 10.15252/embj.201695709
![]() |
[46] |
Huang LC, Lin W, Yagami M, et al. (2010) Validation of cell density and viability assays using Cedex automated cell counter. Biologicals 38: 393-400. doi: 10.1016/j.biologicals.2010.01.009
![]() |
[47] |
Sabantina L, Rodríguez-Cano MA, Klöcker M, et al. (2018) Fixing PAN nanofiber mats during stabilization for carbonization and creating novel metal/carbon composites. Polymers 10: 735. doi: 10.3390/polym10070735
![]() |
[48] |
Baek M, Kim MK, Cho HJ, et al. (2011) Factors influencing the cytotoxicity of zinc oxide nanoparticles: particle size and surface charge. J Phys Conf Ser 304: 012044. doi: 10.1088/1742-6596/304/1/012044
![]() |
[49] |
Sing S (2019) Zinc oxide nanoparticles impacts: cytotoxicity, genotoxicity, development toxicity, and neurotoxicity. Toxicol Mech Methods 29: 300-311. doi: 10.1080/15376516.2018.1553221
![]() |
[50] |
Kuebodeaux RE, Bernazzani P, Nguyen TTM (2018) Cytotoxic and membrane cholesterol effects of ultraviolet irradiation and zinc oxide nanoparticles on Chinese hamster ovary cells. Molecules 23: 2979. doi: 10.3390/molecules23112979
![]() |
[51] |
Zukiene R, Snitka V (2015) Zinc oxide nanoparticle and bovine serum albumin interaction andnanoparticles influence on cytotoxicity in vitro. Colloids Surf B 135: 316-323. doi: 10.1016/j.colsurfb.2015.07.054
![]() |
1. | Xin Du, Quansheng Liu, Yuanhong Bi, Bifurcation analysis of a two–dimensional p53 gene regulatory network without and with time delay, 2023, 32, 2688-1594, 293, 10.3934/era.2024014 | |
2. | Huazhou Mo, Yuanfu Shao, Stability and bifurcation analysis of a delayed stage-structured predator–prey model with fear, additional food, and cooperative behavior in both species, 2025, 2025, 2731-4235, 10.1186/s13662-025-03879-y |
Algo.1 | Algo.2 | |||||
Test Image | SNR | PSNR | SSIM | SNR | PSNR | SSIM |
A | 16.74 | 19.03 | 0.765 | 16.66 | 18.95 | 0.760 |
B | 16.65 | 21.98 | 0.911 | 16.59 | 21.93 | 0.910 |
C | 20.93 | 22.76 | 0.913 | 20.87 | 22.70 | 0.912 |
D | 18.80 | 21.71 | 0.931 | 18.68 | 21.58 | 0.929 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 3 | 11 | 0.020026 | 0 | 32 | 128 | 0.15285 | 5.77E-07 |
z2 | 2 | 7 | 0.022233 | 0 | 23 | 92 | 0.046757 | 1.03E-07 | |
z3 | 3 | 11 | 0.028924 | 0.00E+00 | 43 | 172 | 0.085067 | 3.24E-07 | |
z4 | 2 | 7 | 0.01272 | 0.00E+00 | 28 | 112 | 0.042162 | 8.50E-07 | |
z5 | 2 | 7 | 0.012594 | 0 | 38 | 152 | 0.082875 | 7.44E-07 | |
z6 | 2 | 7 | 0.006795 | 0.00E+00 | 34 | 136 | 0.061034 | 4.36E-07 | |
z7 | 29 | 116 | 0.098046 | 3.71E-08 | 62 | 248 | 0.1162 | 3.84E-07 | |
5000 | z1 | 2 | 7 | 0.1681 | 0 | 16 | 64 | 0.097823 | 4.98E-07 |
z2 | 2 | 7 | 0.07673 | 0 | 27 | 108 | 0.16998 | 5.89E-08 | |
z3 | 2 | 7 | 0.019262 | 0.00E+00 | 34 | 136 | 0.43167 | 8.96E-07 | |
z4 | 2 | 7 | 0.041163 | 0.00E+00 | 43 | 172 | 0.24401 | 4.77E-07 | |
z5 | 2 | 7 | 0.035437 | 0.00E+00 | 36 | 144 | 0.28409 | 4.72E-07 | |
z6 | 2 | 7 | 0.031377 | 0 | 25 | 100 | 0.1577 | 8.50E-07 | |
z7 | 68 | 272 | 1.5225 | 2.22E-08 | NaN | NaN | NaN | NaN | |
10000 | z1 | 2 | 7 | 0.067548 | 0 | 7 | 28 | 0.080462 | 7.04E-07 |
z2 | 2 | 7 | 0.02502 | 0 | 24 | 96 | 0.9236 | 2.84E-07 | |
z3 | 2 | 7 | 0.037267 | 0.00E+00 | 21 | 84 | 0.82591 | 6.94E-07 | |
z4 | 2 | 7 | 0.027143 | 0 | 38 | 152 | 0.97602 | 5.16E-07 | |
z5 | 2 | 7 | 0.070627 | 0 | 28 | 112 | 0.46927 | 8.68E-07 | |
z6 | 2 | 7 | 0.052355 | 0 | 25 | 100 | 0.28425 | 8.52E-07 | |
z7 | 107 | 428 | 9.536 | 3.42E-08 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.35904 | 0 | 7 | 28 | 0.29707 | 2.32E-07 |
z2 | 2 | 7 | 0.24819 | 0 | 15 | 60 | 1.212 | 2.10E-07 | |
z3 | 2 | 7 | 0.21212 | 0.00E+00 | 7 | 28 | 0.33872 | 7.76E-07 | |
z4 | 2 | 7 | 0.265 | 0.00E+00 | 24 | 96 | 1.2315 | 7.36E-07 | |
z5 | 2 | 7 | 0.22679 | 0.00E+00 | 21 | 84 | 0.98662 | 9.19E-07 | |
z6 | 2 | 7 | 0.46048 | 0.00E+00 | 8 | 32 | 0.44742 | 4.62E-07 | |
z7 | 353 | 1412 | 85.8011 | 1.12E-11 | NaN | NaN | NaN | NaN | |
100000 | z1 | 2 | 7 | 0.26127 | 0 | 7 | 28 | 0.66487 | 2.45E-07 |
z2 | 2 | 7 | 0.42916 | 0 | 14 | 56 | 1.9555 | 4.72E-07 | |
z3 | 2 | 7 | 0.29924 | 0.00E+00 | 7 | 28 | 0.65463 | 8.36E-07 | |
z4 | 2 | 7 | 0.47753 | 0 | 28 | 112 | 4.5812 | 5.94E-07 | |
z5 | 2 | 7 | 0.28228 | 0.00E+00 | 17 | 68 | 2.0596 | 5.23E-07 | |
z6 | 2 | 7 | 0.45284 | 0.00E+00 | 8 | 32 | 1.4187 | 3.26E-07 | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 7 | 22 | 0.047242 | 1.58E-09 | 4 | 12 | 0.075993 | 5.17E-07 |
z2 | 7 | 22 | 0.011612 | 2.12E-09 | 5 | 15 | 0.01685 | 6.04E-09 | |
z3 | 6 | 19 | 0.008748 | 7.52E-09 | 5 | 15 | 0.009081 | 4.37E-07 | |
z4 | 8 | 25 | 0.008643 | 1.95E-09 | 6 | 18 | 0.009114 | 1.52E-07 | |
z5 | 6 | 19 | 0.010119 | 8.43E-09 | 7 | 21 | 0.013185 | 1.10E-09 | |
z6 | 9 | 28 | 0.009592 | 1.04E-09 | 7 | 21 | 0.014685 | 1.74E-08 | |
z7 | 44 | 169 | 0.043234 | 9.47E-07 | 69 | 261 | 0.22456 | 6.30E-07 | |
5000 | z1 | 6 | 20 | 0.062266 | 2.97E-07 | 4 | 12 | 0.012773 | 1.75E-07 |
z2 | 6 | 20 | 0.031005 | 4.05E-07 | 5 | 15 | 0.019072 | 6.27E-10 | |
z3 | 6 | 19 | 0.022469 | 9.12E-10 | 5 | 15 | 0.03412 | 1.42E-07 | |
z4 | 7 | 23 | 0.048441 | 3.74E-07 | 6 | 18 | 0.040398 | 3.94E-08 | |
z5 | 6 | 19 | 0.032782 | 1.42E-09 | 6 | 18 | 0.030696 | 4.05E-07 | |
z6 | 7 | 22 | 0.038421 | 7.12E-09 | 7 | 21 | 0.02232 | 2.36E-09 | |
z7 | 45 | 169 | 0.32315 | 1.74E-07 | 75 | 290 | 0.68505 | 9.20E-07 | |
10000 | z1 | 5 | 16 | 0.065175 | 9.23E-09 | 4 | 12 | 0.05281 | 1.21E-07 |
z2 | 6 | 21 | 0.072794 | 3.06E-07 | 5 | 15 | 0.055137 | 2.79E-10 | |
z3 | 6 | 19 | 0.036537 | 4.32E-10 | 5 | 15 | 0.038347 | 9.73E-08 | |
z4 | 7 | 24 | 0.054625 | 2.82E-07 | 6 | 18 | 0.057504 | 2.56E-08 | |
z5 | 6 | 20 | 0.09281 | 7.38E-10 | 6 | 18 | 0.053546 | 2.93E-07 | |
z6 | 7 | 22 | 0.098951 | 4.21E-09 | 7 | 21 | 0.05207 | 1.24E-09 | |
z7 | 34 | 133 | 0.35652 | 8.45E-07 | 75 | 286 | 1.1715 | 8.81E-07 | |
50000 | z1 | 7 | 26 | 1.0892 | 1.84E-07 | 4 | 12 | 0.072347 | 6.32E-08 |
z2 | 9 | 34 | 0.57121 | 3.87E-07 | 5 | 16 | 0.17135 | 6.75E-11 | |
z3 | 6 | 21 | 0.17777 | 5.88E-07 | 5 | 15 | 0.30908 | 4.87E-08 | |
z4 | 10 | 37 | 0.79714 | 3.60E-07 | 6 | 18 | 0.30538 | 1.11E-08 | |
z5 | 7 | 25 | 0.14544 | 1.16E-07 | 6 | 18 | 0.17986 | 1.84E-07 | |
z6 | 8 | 28 | 0.24313 | 7.93E-07 | 7 | 21 | 0.11731 | 4.01E-10 | |
z7 | 36 | 141 | 1.1389 | 1.07E-07 | 87 | 326 | 3.3093 | 3.83E-07 | |
100000 | z1 | 7 | 26 | 0.35609 | 2.56E-07 | 4 | 12 | 0.23409 | 5.40E-08 |
z2 | 9 | 34 | 0.43666 | 5.47E-07 | 5 | 16 | 0.3152 | 4.27E-11 | |
z3 | 6 | 21 | 0.31721 | 7.65E-07 | 5 | 15 | 0.28597 | 4.05E-08 | |
z4 | 10 | 37 | 0.53074 | 5.09E-07 | 6 | 18 | 0.23003 | 8.15E-09 | |
z5 | 7 | 25 | 0.27827 | 1.55E-07 | 6 | 18 | 0.45582 | 1.80E-07 | |
z6 | 9 | 32 | 0.5333 | 1.09E-07 | 7 | 22 | 0.2709 | 2.71E-10 | |
z7 | 31 | 121 | 1.7511 | 5.10E-07 | 81 | 306 | 6.1345 | 9.16E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 6 | 0.007199 | 0 | 2 | 6 | 0.026849 | 0 |
z2 | 2 | 6 | 0.00552 | 0 | 2 | 6 | 0.003173 | 0 | |
z3 | 2 | 6 | 0.006377 | 0 | 2 | 6 | 0.006714 | 0 | |
z4 | 3 | 11 | 0.017561 | 0.00E+00 | 2 | 6 | 0.005403 | 0 | |
z5 | 3 | 11 | 0.007556 | 0.00E+00 | 2 | 6 | 0.009761 | 0 | |
z6 | 3 | 11 | 0.008376 | 0 | 2 | 6 | 0.003285 | 0 | |
z7 | 16 | 49 | 0.043387 | 2.91E-07 | 2 | 6 | 0.005238 | 0 | |
5000 | z1 | 2 | 6 | 0.024798 | 0 | 2 | 6 | 0.037672 | 0 |
z2 | 2 | 6 | 0.017882 | 0 | 2 | 6 | 0.016857 | 0 | |
z3 | 2 | 6 | 0.014761 | 0 | 2 | 6 | 0.016971 | 0 | |
z4 | 3 | 11 | 0.021926 | 0.00E+00 | 2 | 6 | 0.024599 | 0 | |
z5 | 3 | 11 | 0.019501 | 0.00E+00 | 2 | 6 | 0.12878 | 0 | |
z6 | 3 | 11 | 0.099645 | 0 | 2 | 6 | 0.016172 | 0 | |
z7 | 21 | 65 | 0.26663 | 8.91E-07 | 2 | 6 | 0.068901 | 0 | |
10000 | z1 | 2 | 6 | 0.053329 | 0 | 2 | 6 | 0.039629 | 0 |
z2 | 2 | 6 | 0.036889 | 0 | 2 | 6 | 0.029941 | 0 | |
z3 | 2 | 6 | 0.02419 | 0 | 2 | 6 | 0.022097 | 0 | |
z4 | 3 | 11 | 0.046062 | 0.00E+00 | 2 | 6 | 0.015668 | 0 | |
z5 | 3 | 11 | 0.17699 | 0.00E+00 | 2 | 6 | 0.1442 | 0 | |
z6 | 3 | 11 | 0.056058 | 0 | 2 | 6 | 0.080865 | 0 | |
z7 | 19 | 58 | 0.42057 | 1.22E-07 | 2 | 6 | 0.052839 | 0 | |
50000 | z1 | 2 | 6 | 0.11901 | 0 | 2 | 6 | 0.27419 | 0 |
z2 | 2 | 6 | 0.10804 | 0 | 2 | 6 | 0.228 | 0 | |
z3 | 2 | 6 | 0.15799 | 0 | 2 | 6 | 0.083129 | 0 | |
z4 | 3 | 11 | 0.27797 | 0.00E+00 | 2 | 6 | 0.09131 | 0 | |
z5 | 3 | 11 | 0.21594 | 0.00E+00 | 2 | 6 | 0.047357 | 0 | |
z6 | 3 | 11 | 0.16137 | 0 | 2 | 6 | 0.049002 | 0 | |
z7 | 21 | 64 | 1.156 | 3.21E-07 | 2 | 6 | 0.12806 | 0 | |
100000 | z1 | 2 | 6 | 0.21976 | 0 | 2 | 6 | 0.15418 | 0 |
z2 | 2 | 6 | 0.19397 | 0 | 2 | 6 | 0.44568 | 0 | |
z3 | 2 | 6 | 0.17969 | 0 | 2 | 6 | 0.79033 | 0 | |
z4 | 3 | 11 | 0.30701 | 0.00E+00 | 2 | 6 | 0.20222 | 0 | |
z5 | 3 | 11 | 0.72994 | 0.00E+00 | 2 | 6 | 0.20959 | 0 | |
z6 | 3 | 11 | 0.36806 | 0 | 2 | 6 | 0.26684 | 0 | |
z7 | 22 | 67 | 1.8809 | 2.86E-07 | 2 | 6 | 0.23472 | 0 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 7 | 0.007686 | 0 | 8 | 31 | 0.025113 | 1.65E-07 |
z2 | 2 | 7 | 0.004973 | 0 | 7 | 28 | 0.007628 | 2.32E-07 | |
z3 | 2 | 7 | 0.004693 | 0.00E+00 | 8 | 32 | 0.009827 | 7.42E-07 | |
z4 | 2 | 7 | 0.005652 | 0.00E+00 | 9 | 35 | 0.012267 | 1.62E-07 | |
z5 | 2 | 7 | 0.007206 | 0.00E+00 | 7 | 28 | 0.012782 | 3.92E-07 | |
z6 | 2 | 7 | 0.005871 | 0.00E+00 | 8 | 32 | 0.016455 | 3.68E-07 | |
z7 | 22 | 87 | 0.030189 | 0.00E+00 | 71 | 284 | 0.045157 | 1.91E-07 | |
5000 | z1 | 2 | 7 | 0.01789 | 0 | 8 | 31 | 0.035804 | 3.68E-07 |
z2 | 2 | 7 | 0.083644 | 0 | 7 | 28 | 0.056219 | 5.20E-07 | |
z3 | 2 | 7 | 0.019787 | 0.00E+00 | 9 | 36 | 0.028182 | 1.66E-07 | |
z4 | 2 | 7 | 0.02077 | 0 | 9 | 35 | 0.028652 | 3.61E-07 | |
z5 | 2 | 7 | 0.023139 | 0 | 7 | 28 | 0.09901 | 8.76E-07 | |
z6 | 2 | 7 | 0.045152 | 0 | 8 | 32 | 0.046074 | 8.22E-07 | |
z7 | 77 | 308 | 0.88375 | 2.85E-07 | 51 | 204 | 0.12808 | 9.55E-07 | |
10000 | z1 | 2 | 7 | 0.025792 | 0 | 8 | 32 | 0.043945 | 5.20E-07 |
z2 | 2 | 7 | 0.020051 | 0 | 7 | 27 | 0.050306 | 7.35E-07 | |
z3 | 2 | 7 | 0.025936 | 0.00E+00 | 9 | 36 | 0.039643 | 2.35E-07 | |
z4 | 2 | 7 | 0.03822 | 0 | 9 | 35 | 0.041378 | 5.11E-07 | |
z5 | 2 | 7 | 0.03849 | 0 | 8 | 32 | 0.13231 | 1.24E-07 | |
z6 | 2 | 7 | 0.031354 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z7 | 101 | 404 | 3.4918 | 4.06E-09 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.091176 | 0 | 9 | 34 | 0.23565 | 0 |
z2 | 2 | 7 | 0.090561 | 0 | NaN | NaN | NaN | NaN | |
z3 | 2 | 7 | 0.13857 | 0.00E+00 | 9 | 35 | 0.12604 | 5.25E-07 | |
z4 | 2 | 7 | 0.10731 | 0.00E+00 | 10 | 38 | 0.426 | 0 | |
z5 | 2 | 7 | 0.14284 | 0.00E+00 | 8 | 31 | 0.47179 | 2.77E-07 | |
z6 | 2 | 7 | 0.29418 | 0.00E+00 | 9 | 35 | 0.21126 | 2.60E-07 | |
z7 | 110 | 439 | 8.6871 | 0 | 44 | 176 | 1.2526 | 3.55E-07 | |
100000 | z1 | 2 | 7 | 0.20371 | 0 | 9 | 36 | 0.2659 | 1.65E-07 |
z2 | 2 | 7 | 0.26727 | 0 | 8 | 30 | 0.48604 | 0 | |
z3 | 2 | 7 | 0.1588 | 0.00E+00 | 9 | 35 | 0.35032 | 7.42E-07 | |
z4 | 2 | 7 | 0.20624 | 0.00E+00 | 10 | 39 | 0.34301 | 1.62E-07 | |
z5 | 2 | 7 | 0.19404 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z6 | 2 | 7 | 0.21718 | 0.00E+00 | 9 | 35 | 0.31142 | 3.68E-07 | |
z7 | 111 | 444 | 18.0039 | 6.11E-08 | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 34 | 127 | 0.026467 | 1.62E-07 | 71 | 263 | 0.16103 | 3.21E-07 |
z2 | 36 | 140 | 0.026972 | 7.43E-07 | 62 | 235 | 0.052281 | 1.13E-07 | |
z3 | 52 | 205 | 0.16096 | 2.58E-07 | 50 | 194 | 0.088863 | 3.72E-07 | |
z4 | 96 | 378 | 0.55079 | 4.35E-07 | NaN | NaN | NaN | NaN | |
z5 | 123 | 492 | 0.48012 | 3.96E-07 | NaN | NaN | NaN | NaN | |
z6 | 196 | 784 | 1.0967 | 6.21E-07 | NaN | NaN | NaN | NaN | |
z7 | 115 | 459 | 0.34961 | 2.89E-07 | NaN | NaN | NaN | NaN | |
5000 | z1 | 59 | 232 | 0.68163 | 2.32E-07 | 63 | 231 | 0.30231 | 3.90E-07 |
z2 | 50 | 188 | 0.29441 | 6.42E-07 | 72 | 282 | 0.18091 | 7.31E-07 | |
z3 | 179 | 709 | 2.2218 | 2.91E-07 | 60 | 232 | 0.14861 | 1.47E-07 | |
z4 | 171 | 684 | 2.9204 | 2.99E-07 | NaN | NaN | NaN | NaN | |
z5 | 297 | 1187 | 5.9983 | 3.31E-07 | NaN | NaN | NaN | NaN | |
z6 | 420 | 1680 | 9.6236 | 1.67E-07 | NaN | NaN | NaN | NaN | |
z7 | 187 | 744 | 3.4767 | 8.43E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 300 | 1.3784 | 1.39E-07 | 75 | 283 | 0.27114 | 2.35E-07 |
z2 | 74 | 283 | 1.5399 | 1.34E-07 | 55 | 208 | 0.20873 | 3.12E-07 | |
z3 | 214 | 843 | 5.0625 | 9.68E-07 | 67 | 259 | 0.65684 | 2.52E-07 | |
z4 | 253 | 1012 | 8.4598 | 5.48E-07 | NaN | NaN | NaN | NaN | |
z5 | 383 | 1531 | 15.2491 | 1.45E-07 | NaN | NaN | NaN | NaN | |
z6 | 575 | 2300 | 24.956 | 4.27E-07 | NaN | NaN | NaN | NaN | |
z7 | 323 | 1291 | 9.6152 | 2.90E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 135 | 534 | 12.3192 | 9.85E-07 | 65 | 253 | 1.9331 | 1.74E-07 |
z2 | 342 | 1357 | 46.7469 | 1.53E-07 | 94 | 369 | 4.3154 | 4.77E-07 | |
z3 | 326 | 1294 | 39.8986 | 4.97E-07 | NaN | NaN | NaN | NaN | |
z4 | 504 | 2016 | 82.9841 | 3.45E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | 602 | 2403 | 97.0953 | 6.65E-07 | NaN | NaN | NaN | NaN | |
100000 | z1 | 164 | 645 | 25.8558 | 1.87E-07 | NaN | NaN | NaN | NaN |
z2 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z3 | 400 | 1590 | 126.0758 | 7.38E-07 | NaN | NaN | NaN | NaN | |
z4 | 636 | 2544 | 240.5206 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 9 | 36 | 0.17935 | 8.25E-07 | 9 | 36 | 0.0153 | 8.24E-07 |
z2 | 9 | 36 | 0.03051 | 7.93E-07 | 9 | 36 | 0.048509 | 7.93E-07 | |
z3 | 9 | 36 | 0.027967 | 6.99E-07 | 9 | 36 | 0.017521 | 6.98E-07 | |
z4 | 9 | 36 | 0.015472 | 4.79E-07 | 9 | 36 | 0.014811 | 4.78E-07 | |
z5 | 9 | 36 | 0.007122 | 3.84E-07 | 9 | 36 | 0.016431 | 3.83E-07 | |
z6 | 9 | 36 | 0.010164 | 2.27E-07 | 9 | 36 | 0.009737 | 2.26E-07 | |
z7 | 9 | 36 | 0.020191 | 7.23E-07 | 9 | 36 | 0.017515 | 7.06E-07 | |
5000 | z1 | 10 | 40 | 0.048118 | 1.85E-07 | 10 | 40 | 0.082844 | 1.85E-07 |
z2 | 10 | 40 | 0.097072 | 1.78E-07 | 10 | 40 | 0.050343 | 1.78E-07 | |
z3 | 10 | 40 | 0.032297 | 1.57E-07 | 10 | 40 | 0.10792 | 1.57E-07 | |
z4 | 10 | 40 | 0.043942 | 1.07E-07 | 10 | 40 | 0.076199 | 1.07E-07 | |
z5 | 9 | 36 | 0.043841 | 8.61E-07 | 9 | 36 | 0.037916 | 8.61E-07 | |
z6 | 9 | 36 | 0.033263 | 5.08E-07 | 9 | 36 | 0.069375 | 5.08E-07 | |
z7 | 10 | 40 | 0.037194 | 1.58E-07 | 10 | 40 | 0.047672 | 1.58E-07 | |
10000 | z1 | 10 | 40 | 0.082406 | 2.62E-07 | 10 | 40 | 0.076648 | 2.62E-07 |
z2 | 10 | 40 | 0.068947 | 2.52E-07 | 10 | 40 | 0.15678 | 2.52E-07 | |
z3 | 10 | 40 | 0.058721 | 2.22E-07 | 10 | 40 | 0.13597 | 2.22E-07 | |
z4 | 10 | 40 | 0.078257 | 1.52E-07 | 10 | 40 | 0.08399 | 1.52E-07 | |
z5 | 10 | 40 | 0.062069 | 1.22E-07 | 10 | 40 | 0.07822 | 1.22E-07 | |
z6 | 9 | 36 | 0.053275 | 7.18E-07 | 9 | 36 | 0.1205 | 7.18E-07 | |
z7 | 10 | 40 | 0.057688 | 2.24E-07 | 10 | 40 | 0.080168 | 2.23E-07 | |
50000 | z1 | 10 | 40 | 0.22352 | 5.85E-07 | 10 | 39 | 0.38243 | 5.85E-07 |
z2 | 10 | 40 | 0.27436 | 5.63E-07 | 10 | 39 | 0.41361 | 5.63E-07 | |
z3 | 10 | 40 | 0.23122 | 4.96E-07 | 10 | 39 | 0.30721 | 4.96E-07 | |
z4 | 10 | 40 | 0.21192 | 3.40E-07 | 10 | 39 | 0.43086 | 3.40E-07 | |
z5 | 10 | 40 | 0.23892 | 2.72E-07 | 10 | 38 | 0.29829 | 1.26E-15 | |
z6 | 10 | 40 | 0.29017 | 1.61E-07 | 10 | 38 | 0.51415 | 6.28E-16 | |
z7 | 10 | 40 | 0.25616 | 5.01E-07 | 10 | 39 | 0.29756 | 5.00E-07 | |
100000 | z1 | 10 | 40 | 0.82944 | 8.28E-07 | 10 | 39 | 1.1183 | 8.28E-07 |
z2 | 10 | 40 | 0.47168 | 7.96E-07 | 10 | 38 | 0.6117 | 6.28E-16 | |
z3 | 10 | 40 | 0.49749 | 7.01E-07 | 10 | 38 | 0.81145 | 6.28E-16 | |
z4 | 10 | 40 | 0.52125 | 4.80E-07 | 10 | 38 | 0.79886 | 0 | |
z5 | 10 | 40 | 0.69499 | 3.85E-07 | 10 | 38 | 0.60219 | 0 | |
z6 | 10 | 40 | 0.47656 | 2.27E-07 | 10 | 38 | 0.72864 | 0 | |
z7 | 10 | 40 | 0.49578 | 7.07E-07 | 10 | 39 | 0.80741 | 7.07E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 5 | 20 | 0.046544 | 3.24E-07 | 5 | 20 | 0.008647 | 3.24E-07 |
z2 | 5 | 20 | 0.009418 | 1.43E-07 | 5 | 20 | 0.013849 | 1.43E-07 | |
z3 | 5 | 20 | 0.038932 | 1.68E-08 | 4 | 16 | 0.015388 | 5.81E-08 | |
z4 | 6 | 24 | 0.01166 | 9.16E-09 | 6 | 24 | 0.010967 | 3.39E-08 | |
z5 | 6 | 24 | 0.010929 | 1.23E-08 | 6 | 24 | 0.0107 | 4.99E-08 | |
z6 | 6 | 23 | 0.01937 | 1.04E-07 | 6 | 23 | 0.014025 | 6.55E-08 | |
z7 | 26 | 104 | 0.032336 | 8.36E-09 | 36 | 144 | 0.12555 | 5.34E-08 | |
5000 | z1 | 5 | 20 | 0.029586 | 7.25E-07 | 5 | 20 | 0.041107 | 7.25E-07 |
z2 | 5 | 20 | 0.027892 | 3.20E-07 | 5 | 20 | 0.038182 | 3.20E-07 | |
z3 | 5 | 20 | 0.035333 | 3.75E-08 | 4 | 16 | 0.12123 | 1.30E-07 | |
z4 | 6 | 24 | 0.032225 | 2.05E-08 | 6 | 24 | 0.05211 | 7.58E-08 | |
z5 | 6 | 24 | 0.026546 | 2.75E-08 | 6 | 24 | 0.038675 | 1.12E-07 | |
z6 | 6 | 23 | 0.032529 | 2.32E-07 | 6 | 23 | 0.081384 | 1.46E-07 | |
z7 | 34 | 136 | 0.24122 | 3.59E-08 | 41 | 164 | 0.29917 | 1.14E-07 | |
10000 | z1 | 6 | 24 | 0.043879 | 5.12E-09 | 6 | 24 | 0.079589 | 5.12E-09 |
z2 | 5 | 20 | 0.036531 | 4.52E-07 | 5 | 20 | 0.1417 | 4.52E-07 | |
z3 | 5 | 20 | 0.050902 | 5.31E-08 | 4 | 16 | 0.045901 | 1.84E-07 | |
z4 | 6 | 24 | 0.054078 | 2.90E-08 | 6 | 24 | 0.059807 | 1.07E-07 | |
z5 | 6 | 24 | 0.052048 | 3.89E-08 | 6 | 24 | 0.099213 | 1.58E-07 | |
z6 | 6 | 23 | 0.04894 | 3.28E-07 | 6 | 23 | 0.054029 | 2.07E-07 | |
z7 | 41 | 164 | 0.30793 | 3.45E-08 | 45 | 180 | 0.92444 | 3.64E-07 | |
50000 | z1 | 6 | 24 | 0.14 | 1.15E-08 | 6 | 24 | 0.26027 | 1.15E-08 |
z2 | 6 | 24 | 0.14343 | 5.06E-09 | 6 | 24 | 0.60276 | 5.06E-09 | |
z3 | 5 | 20 | 0.15201 | 1.19E-07 | 4 | 16 | 0.17247 | 4.11E-07 | |
z4 | 6 | 24 | 0.34794 | 6.48E-08 | 6 | 24 | 0.22999 | 2.40E-07 | |
z5 | 6 | 24 | 0.15433 | 8.70E-08 | 6 | 24 | 0.38048 | 3.53E-07 | |
z6 | 6 | 23 | 0.1425 | 7.35E-07 | 6 | 23 | 0.2271 | 4.63E-07 | |
z7 | 29 | 116 | 1.295 | 9.41E-09 | 44 | 176 | 2.2436 | 7.06E-07 | |
100000 | z1 | 6 | 24 | 0.39791 | 1.62E-08 | 6 | 24 | 0.94834 | 1.62E-08 |
z2 | 6 | 24 | 0.47548 | 7.15E-09 | 6 | 24 | 0.43453 | 7.15E-09 | |
z3 | 5 | 20 | 0.48174 | 1.68E-07 | 4 | 16 | 0.29517 | 5.81E-07 | |
z4 | 6 | 24 | 0.26721 | 9.16E-08 | 6 | 24 | 0.55119 | 3.39E-07 | |
z5 | 6 | 24 | 0.28512 | 1.23E-07 | 6 | 24 | 0.61073 | 4.99E-07 | |
z6 | 7 | 27 | 0.5385 | 5.19E-09 | 6 | 23 | 0.42035 | 6.55E-07 | |
z7 | 29 | 116 | 1.6021 | 1.19E-08 | 41 | 164 | 3.9953 | 9.23E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 66 | 264 | 0.934 | 3.48E-07 | NaN | NaN | NaN | NaN |
z2 | 101 | 404 | 0.99428 | 4.28E-07 | 41 | 164 | 0.75214 | 4.29E-07 | |
z3 | 40 | 160 | 0.40127 | 3.33E-07 | NaN | NaN | NaN | NaN | |
z4 | 39 | 156 | 0.5071 | 5.07E-07 | 39 | 156 | 0.71207 | 3.83E-07 | |
z5 | 36 | 144 | 0.61923 | 4.69E-07 | 35 | 140 | 1.4123 | 4.07E-07 | |
z6 | 4 | 14 | 0.071864 | NaN | 4 | 14 | 0.059454 | NaN | |
z7 | 23 | 89 | 0.48051 | NaN | NaN | NaN | NaN | NaN | |
5000 | z1 | 52 | 208 | 2.7649 | 2.91E-07 | NaN | NaN | NaN | NaN |
z2 | 44 | 176 | 2.1027 | 3.54E-07 | NaN | NaN | NaN | NaN | |
z3 | 42 | 168 | 2.1325 | 2.95E-07 | NaN | NaN | NaN | NaN | |
z4 | 37 | 148 | 2.0738 | 3.41E-07 | NaN | NaN | NaN | NaN | |
z5 | 16 | 60 | 0.64982 | NaN | NaN | NaN | NaN | NaN | |
z6 | 20 | 76 | 0.98188 | NaN | NaN | NaN | NaN | NaN | |
z7 | 301 | 1202 | 18.7543 | 4.37E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 303 | 9.6495 | 3.64E-07 | NaN | NaN | NaN | NaN |
z2 | 71 | 284 | 8.0859 | 3.74E-07 | NaN | NaN | NaN | NaN | |
z3 | 62 | 248 | 7.1755 | 3.27E-07 | NaN | NaN | NaN | NaN | |
z4 | 48 | 192 | 4.1575 | 4.42E-07 | NaN | NaN | NaN | NaN | |
z5 | 15 | 55 | 0.93456 | NaN | NaN | NaN | NaN | NaN | |
z6 | 123 | 490 | 12.4072 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z7 | 307 | 1226 | 35.579 | 3.46E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 24 | 89 | 8.5017 | NaN | NaN | NaN | NaN | NaN |
z2 | 89 | 355 | 45.0395 | 4.34E-07 | NaN | NaN | NaN | NaN | |
z3 | 65 | 260 | 28.4752 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z4 | 431 | 1718 | 135.7493 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z5 | 6 | 21 | 2.1067 | NaN | NaN | NaN | NaN | NaN | |
z6 | 6 | 21 | 1.8349 | NaN | NaN | NaN | NaN | NaN | |
z7 | 7 | 24 | 1.8872 | NaN | NaN | NaN | NaN | NaN | |
100000 | z1 | 34 | 130 | 31.5135 | NaN | NaN | NaN | NaN | NaN |
z2 | 5 | 17 | 1.9076 | NaN | NaN | NaN | NaN | NaN | |
z3 | 87 | 332 | 64.5816 | 3.00E-07 | NaN | NaN | NaN | NaN | |
z4 | 76 | 303 | 68.3533 | 4.49E-07 | NaN | NaN | NaN | NaN | |
z5 | 5 | 17 | 2.2305 | NaN | NaN | NaN | NaN | NaN | |
z6 | 5 | 17 | 2.5293 | NaN | NaN | NaN | NaN | NaN | |
z7 | 6 | 21 | 3.1078 | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 10 | 34 | 0.032445 | 1.06E-07 | 10 | 34 | 0.005932 | 1.06E-07 |
z2 | 10 | 34 | 0.008239 | 1.06E-07 | 10 | 34 | 0.010335 | 1.06E-07 | |
z3 | 10 | 34 | 0.0073 | 1.06E-07 | 10 | 34 | 0.008407 | 1.06E-07 | |
z4 | 10 | 34 | 0.008495 | 1.06E-07 | 10 | 34 | 0.010614 | 1.06E-07 | |
z5 | 10 | 34 | 0.00772 | 1.06E-07 | 10 | 34 | 0.00775 | 1.06E-07 | |
z6 | 10 | 34 | 0.011383 | 1.06E-07 | 10 | 35 | 0.009311 | 1.06E-07 | |
z7 | 67 | 213 | 0.024778 | 9.71E-07 | 10 | 34 | 0.008864 | 1.06E-07 | |
5000 | z1 | 7 | 25 | 0.022534 | 6.89E-08 | 7 | 25 | 0.027033 | 6.89E-08 |
z2 | 7 | 25 | 0.032305 | 6.89E-08 | 7 | 25 | 0.02838 | 6.89E-08 | |
z3 | 7 | 25 | 0.026468 | 6.89E-08 | 7 | 25 | 0.068469 | 6.89E-08 | |
z4 | 7 | 25 | 0.034453 | 6.89E-08 | 7 | 26 | 0.037886 | 6.89E-08 | |
z5 | 7 | 25 | 0.021703 | 6.89E-08 | 7 | 26 | 0.037186 | 6.89E-08 | |
z6 | 7 | 25 | 0.027352 | 6.89E-08 | 7 | 26 | 0.077955 | 6.89E-08 | |
z7 | 20 | 66 | 0.061189 | 9.72E-07 | 7 | 25 | 0.037992 | 6.89E-08 | |
10000 | z1 | 6 | 22 | 0.07498 | 8.13E-08 | 6 | 22 | 0.054682 | 8.13E-08 |
z2 | 6 | 22 | 0.047478 | 8.13E-08 | 6 | 22 | 0.21797 | 8.13E-08 | |
z3 | 6 | 22 | 0.052347 | 8.13E-08 | 6 | 22 | 0.081579 | 8.13E-08 | |
z4 | 6 | 22 | 0.047644 | 8.13E-08 | 6 | 23 | 0.085064 | 8.13E-08 | |
z5 | 6 | 22 | 0.068304 | 8.13E-08 | 6 | 23 | 0.19028 | 8.13E-08 | |
z6 | 6 | 22 | 0.042771 | 8.13E-08 | 6 | 23 | 0.15365 | 8.13E-08 | |
z7 | 12 | 41 | 0.074071 | 9.08E-07 | 6 | 22 | 0.056989 | 8.13E-08 | |
50000 | z1 | 5 | 19 | 0.22112 | 1.41E-07 | 5 | 19 | 0.60662 | 1.41E-07 |
z2 | 5 | 19 | 0.21638 | 1.41E-07 | 5 | 19 | 0.33244 | 1.41E-07 | |
z3 | 5 | 19 | 0.22186 | 1.41E-07 | 5 | 20 | 0.8389 | 1.41E-07 | |
z4 | 5 | 19 | 0.37207 | 1.41E-07 | 5 | 20 | 0.63139 | 1.41E-07 | |
z5 | 5 | 19 | 0.36107 | 1.41E-07 | 5 | 20 | 1.046 | 1.41E-07 | |
z6 | 5 | 19 | 0.27063 | 1.41E-07 | 5 | 20 | 1.4673 | 1.41E-07 | |
z7 | 59 | 235 | 2.7862 | 4.11E-07 | 5 | 19 | 0.57234 | 1.41E-07 | |
100000 | z1 | 6 | 23 | 0.93893 | 2.10E-07 | 6 | 23 | 1.3525 | 2.10E-07 |
z2 | 6 | 23 | 0.60445 | 2.10E-07 | 6 | 24 | 1.5313 | 2.10E-07 | |
z3 | 6 | 23 | 0.71683 | 2.10E-07 | 6 | 24 | 1.6022 | 2.10E-07 | |
z4 | 6 | 23 | 0.57114 | 2.10E-07 | 6 | 24 | 1.7882 | 2.10E-07 | |
z5 | 6 | 23 | 0.57099 | 2.10E-07 | 6 | 24 | 1.878 | 2.10E-07 | |
z6 | 6 | 23 | 0.69104 | 2.10E-07 | 6 | 24 | 1.9634 | 2.10E-07 | |
z7 | 34 | 135 | 4.3899 | 4.52E-07 | 6 | 23 | 1.4688 | 2.10E-07 |
Algo.1 | Algo.2 | |||||
Test Image | SNR | PSNR | SSIM | SNR | PSNR | SSIM |
A | 16.74 | 19.03 | 0.765 | 16.66 | 18.95 | 0.760 |
B | 16.65 | 21.98 | 0.911 | 16.59 | 21.93 | 0.910 |
C | 20.93 | 22.76 | 0.913 | 20.87 | 22.70 | 0.912 |
D | 18.80 | 21.71 | 0.931 | 18.68 | 21.58 | 0.929 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 3 | 11 | 0.020026 | 0 | 32 | 128 | 0.15285 | 5.77E-07 |
z2 | 2 | 7 | 0.022233 | 0 | 23 | 92 | 0.046757 | 1.03E-07 | |
z3 | 3 | 11 | 0.028924 | 0.00E+00 | 43 | 172 | 0.085067 | 3.24E-07 | |
z4 | 2 | 7 | 0.01272 | 0.00E+00 | 28 | 112 | 0.042162 | 8.50E-07 | |
z5 | 2 | 7 | 0.012594 | 0 | 38 | 152 | 0.082875 | 7.44E-07 | |
z6 | 2 | 7 | 0.006795 | 0.00E+00 | 34 | 136 | 0.061034 | 4.36E-07 | |
z7 | 29 | 116 | 0.098046 | 3.71E-08 | 62 | 248 | 0.1162 | 3.84E-07 | |
5000 | z1 | 2 | 7 | 0.1681 | 0 | 16 | 64 | 0.097823 | 4.98E-07 |
z2 | 2 | 7 | 0.07673 | 0 | 27 | 108 | 0.16998 | 5.89E-08 | |
z3 | 2 | 7 | 0.019262 | 0.00E+00 | 34 | 136 | 0.43167 | 8.96E-07 | |
z4 | 2 | 7 | 0.041163 | 0.00E+00 | 43 | 172 | 0.24401 | 4.77E-07 | |
z5 | 2 | 7 | 0.035437 | 0.00E+00 | 36 | 144 | 0.28409 | 4.72E-07 | |
z6 | 2 | 7 | 0.031377 | 0 | 25 | 100 | 0.1577 | 8.50E-07 | |
z7 | 68 | 272 | 1.5225 | 2.22E-08 | NaN | NaN | NaN | NaN | |
10000 | z1 | 2 | 7 | 0.067548 | 0 | 7 | 28 | 0.080462 | 7.04E-07 |
z2 | 2 | 7 | 0.02502 | 0 | 24 | 96 | 0.9236 | 2.84E-07 | |
z3 | 2 | 7 | 0.037267 | 0.00E+00 | 21 | 84 | 0.82591 | 6.94E-07 | |
z4 | 2 | 7 | 0.027143 | 0 | 38 | 152 | 0.97602 | 5.16E-07 | |
z5 | 2 | 7 | 0.070627 | 0 | 28 | 112 | 0.46927 | 8.68E-07 | |
z6 | 2 | 7 | 0.052355 | 0 | 25 | 100 | 0.28425 | 8.52E-07 | |
z7 | 107 | 428 | 9.536 | 3.42E-08 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.35904 | 0 | 7 | 28 | 0.29707 | 2.32E-07 |
z2 | 2 | 7 | 0.24819 | 0 | 15 | 60 | 1.212 | 2.10E-07 | |
z3 | 2 | 7 | 0.21212 | 0.00E+00 | 7 | 28 | 0.33872 | 7.76E-07 | |
z4 | 2 | 7 | 0.265 | 0.00E+00 | 24 | 96 | 1.2315 | 7.36E-07 | |
z5 | 2 | 7 | 0.22679 | 0.00E+00 | 21 | 84 | 0.98662 | 9.19E-07 | |
z6 | 2 | 7 | 0.46048 | 0.00E+00 | 8 | 32 | 0.44742 | 4.62E-07 | |
z7 | 353 | 1412 | 85.8011 | 1.12E-11 | NaN | NaN | NaN | NaN | |
100000 | z1 | 2 | 7 | 0.26127 | 0 | 7 | 28 | 0.66487 | 2.45E-07 |
z2 | 2 | 7 | 0.42916 | 0 | 14 | 56 | 1.9555 | 4.72E-07 | |
z3 | 2 | 7 | 0.29924 | 0.00E+00 | 7 | 28 | 0.65463 | 8.36E-07 | |
z4 | 2 | 7 | 0.47753 | 0 | 28 | 112 | 4.5812 | 5.94E-07 | |
z5 | 2 | 7 | 0.28228 | 0.00E+00 | 17 | 68 | 2.0596 | 5.23E-07 | |
z6 | 2 | 7 | 0.45284 | 0.00E+00 | 8 | 32 | 1.4187 | 3.26E-07 | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 7 | 22 | 0.047242 | 1.58E-09 | 4 | 12 | 0.075993 | 5.17E-07 |
z2 | 7 | 22 | 0.011612 | 2.12E-09 | 5 | 15 | 0.01685 | 6.04E-09 | |
z3 | 6 | 19 | 0.008748 | 7.52E-09 | 5 | 15 | 0.009081 | 4.37E-07 | |
z4 | 8 | 25 | 0.008643 | 1.95E-09 | 6 | 18 | 0.009114 | 1.52E-07 | |
z5 | 6 | 19 | 0.010119 | 8.43E-09 | 7 | 21 | 0.013185 | 1.10E-09 | |
z6 | 9 | 28 | 0.009592 | 1.04E-09 | 7 | 21 | 0.014685 | 1.74E-08 | |
z7 | 44 | 169 | 0.043234 | 9.47E-07 | 69 | 261 | 0.22456 | 6.30E-07 | |
5000 | z1 | 6 | 20 | 0.062266 | 2.97E-07 | 4 | 12 | 0.012773 | 1.75E-07 |
z2 | 6 | 20 | 0.031005 | 4.05E-07 | 5 | 15 | 0.019072 | 6.27E-10 | |
z3 | 6 | 19 | 0.022469 | 9.12E-10 | 5 | 15 | 0.03412 | 1.42E-07 | |
z4 | 7 | 23 | 0.048441 | 3.74E-07 | 6 | 18 | 0.040398 | 3.94E-08 | |
z5 | 6 | 19 | 0.032782 | 1.42E-09 | 6 | 18 | 0.030696 | 4.05E-07 | |
z6 | 7 | 22 | 0.038421 | 7.12E-09 | 7 | 21 | 0.02232 | 2.36E-09 | |
z7 | 45 | 169 | 0.32315 | 1.74E-07 | 75 | 290 | 0.68505 | 9.20E-07 | |
10000 | z1 | 5 | 16 | 0.065175 | 9.23E-09 | 4 | 12 | 0.05281 | 1.21E-07 |
z2 | 6 | 21 | 0.072794 | 3.06E-07 | 5 | 15 | 0.055137 | 2.79E-10 | |
z3 | 6 | 19 | 0.036537 | 4.32E-10 | 5 | 15 | 0.038347 | 9.73E-08 | |
z4 | 7 | 24 | 0.054625 | 2.82E-07 | 6 | 18 | 0.057504 | 2.56E-08 | |
z5 | 6 | 20 | 0.09281 | 7.38E-10 | 6 | 18 | 0.053546 | 2.93E-07 | |
z6 | 7 | 22 | 0.098951 | 4.21E-09 | 7 | 21 | 0.05207 | 1.24E-09 | |
z7 | 34 | 133 | 0.35652 | 8.45E-07 | 75 | 286 | 1.1715 | 8.81E-07 | |
50000 | z1 | 7 | 26 | 1.0892 | 1.84E-07 | 4 | 12 | 0.072347 | 6.32E-08 |
z2 | 9 | 34 | 0.57121 | 3.87E-07 | 5 | 16 | 0.17135 | 6.75E-11 | |
z3 | 6 | 21 | 0.17777 | 5.88E-07 | 5 | 15 | 0.30908 | 4.87E-08 | |
z4 | 10 | 37 | 0.79714 | 3.60E-07 | 6 | 18 | 0.30538 | 1.11E-08 | |
z5 | 7 | 25 | 0.14544 | 1.16E-07 | 6 | 18 | 0.17986 | 1.84E-07 | |
z6 | 8 | 28 | 0.24313 | 7.93E-07 | 7 | 21 | 0.11731 | 4.01E-10 | |
z7 | 36 | 141 | 1.1389 | 1.07E-07 | 87 | 326 | 3.3093 | 3.83E-07 | |
100000 | z1 | 7 | 26 | 0.35609 | 2.56E-07 | 4 | 12 | 0.23409 | 5.40E-08 |
z2 | 9 | 34 | 0.43666 | 5.47E-07 | 5 | 16 | 0.3152 | 4.27E-11 | |
z3 | 6 | 21 | 0.31721 | 7.65E-07 | 5 | 15 | 0.28597 | 4.05E-08 | |
z4 | 10 | 37 | 0.53074 | 5.09E-07 | 6 | 18 | 0.23003 | 8.15E-09 | |
z5 | 7 | 25 | 0.27827 | 1.55E-07 | 6 | 18 | 0.45582 | 1.80E-07 | |
z6 | 9 | 32 | 0.5333 | 1.09E-07 | 7 | 22 | 0.2709 | 2.71E-10 | |
z7 | 31 | 121 | 1.7511 | 5.10E-07 | 81 | 306 | 6.1345 | 9.16E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 6 | 0.007199 | 0 | 2 | 6 | 0.026849 | 0 |
z2 | 2 | 6 | 0.00552 | 0 | 2 | 6 | 0.003173 | 0 | |
z3 | 2 | 6 | 0.006377 | 0 | 2 | 6 | 0.006714 | 0 | |
z4 | 3 | 11 | 0.017561 | 0.00E+00 | 2 | 6 | 0.005403 | 0 | |
z5 | 3 | 11 | 0.007556 | 0.00E+00 | 2 | 6 | 0.009761 | 0 | |
z6 | 3 | 11 | 0.008376 | 0 | 2 | 6 | 0.003285 | 0 | |
z7 | 16 | 49 | 0.043387 | 2.91E-07 | 2 | 6 | 0.005238 | 0 | |
5000 | z1 | 2 | 6 | 0.024798 | 0 | 2 | 6 | 0.037672 | 0 |
z2 | 2 | 6 | 0.017882 | 0 | 2 | 6 | 0.016857 | 0 | |
z3 | 2 | 6 | 0.014761 | 0 | 2 | 6 | 0.016971 | 0 | |
z4 | 3 | 11 | 0.021926 | 0.00E+00 | 2 | 6 | 0.024599 | 0 | |
z5 | 3 | 11 | 0.019501 | 0.00E+00 | 2 | 6 | 0.12878 | 0 | |
z6 | 3 | 11 | 0.099645 | 0 | 2 | 6 | 0.016172 | 0 | |
z7 | 21 | 65 | 0.26663 | 8.91E-07 | 2 | 6 | 0.068901 | 0 | |
10000 | z1 | 2 | 6 | 0.053329 | 0 | 2 | 6 | 0.039629 | 0 |
z2 | 2 | 6 | 0.036889 | 0 | 2 | 6 | 0.029941 | 0 | |
z3 | 2 | 6 | 0.02419 | 0 | 2 | 6 | 0.022097 | 0 | |
z4 | 3 | 11 | 0.046062 | 0.00E+00 | 2 | 6 | 0.015668 | 0 | |
z5 | 3 | 11 | 0.17699 | 0.00E+00 | 2 | 6 | 0.1442 | 0 | |
z6 | 3 | 11 | 0.056058 | 0 | 2 | 6 | 0.080865 | 0 | |
z7 | 19 | 58 | 0.42057 | 1.22E-07 | 2 | 6 | 0.052839 | 0 | |
50000 | z1 | 2 | 6 | 0.11901 | 0 | 2 | 6 | 0.27419 | 0 |
z2 | 2 | 6 | 0.10804 | 0 | 2 | 6 | 0.228 | 0 | |
z3 | 2 | 6 | 0.15799 | 0 | 2 | 6 | 0.083129 | 0 | |
z4 | 3 | 11 | 0.27797 | 0.00E+00 | 2 | 6 | 0.09131 | 0 | |
z5 | 3 | 11 | 0.21594 | 0.00E+00 | 2 | 6 | 0.047357 | 0 | |
z6 | 3 | 11 | 0.16137 | 0 | 2 | 6 | 0.049002 | 0 | |
z7 | 21 | 64 | 1.156 | 3.21E-07 | 2 | 6 | 0.12806 | 0 | |
100000 | z1 | 2 | 6 | 0.21976 | 0 | 2 | 6 | 0.15418 | 0 |
z2 | 2 | 6 | 0.19397 | 0 | 2 | 6 | 0.44568 | 0 | |
z3 | 2 | 6 | 0.17969 | 0 | 2 | 6 | 0.79033 | 0 | |
z4 | 3 | 11 | 0.30701 | 0.00E+00 | 2 | 6 | 0.20222 | 0 | |
z5 | 3 | 11 | 0.72994 | 0.00E+00 | 2 | 6 | 0.20959 | 0 | |
z6 | 3 | 11 | 0.36806 | 0 | 2 | 6 | 0.26684 | 0 | |
z7 | 22 | 67 | 1.8809 | 2.86E-07 | 2 | 6 | 0.23472 | 0 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 2 | 7 | 0.007686 | 0 | 8 | 31 | 0.025113 | 1.65E-07 |
z2 | 2 | 7 | 0.004973 | 0 | 7 | 28 | 0.007628 | 2.32E-07 | |
z3 | 2 | 7 | 0.004693 | 0.00E+00 | 8 | 32 | 0.009827 | 7.42E-07 | |
z4 | 2 | 7 | 0.005652 | 0.00E+00 | 9 | 35 | 0.012267 | 1.62E-07 | |
z5 | 2 | 7 | 0.007206 | 0.00E+00 | 7 | 28 | 0.012782 | 3.92E-07 | |
z6 | 2 | 7 | 0.005871 | 0.00E+00 | 8 | 32 | 0.016455 | 3.68E-07 | |
z7 | 22 | 87 | 0.030189 | 0.00E+00 | 71 | 284 | 0.045157 | 1.91E-07 | |
5000 | z1 | 2 | 7 | 0.01789 | 0 | 8 | 31 | 0.035804 | 3.68E-07 |
z2 | 2 | 7 | 0.083644 | 0 | 7 | 28 | 0.056219 | 5.20E-07 | |
z3 | 2 | 7 | 0.019787 | 0.00E+00 | 9 | 36 | 0.028182 | 1.66E-07 | |
z4 | 2 | 7 | 0.02077 | 0 | 9 | 35 | 0.028652 | 3.61E-07 | |
z5 | 2 | 7 | 0.023139 | 0 | 7 | 28 | 0.09901 | 8.76E-07 | |
z6 | 2 | 7 | 0.045152 | 0 | 8 | 32 | 0.046074 | 8.22E-07 | |
z7 | 77 | 308 | 0.88375 | 2.85E-07 | 51 | 204 | 0.12808 | 9.55E-07 | |
10000 | z1 | 2 | 7 | 0.025792 | 0 | 8 | 32 | 0.043945 | 5.20E-07 |
z2 | 2 | 7 | 0.020051 | 0 | 7 | 27 | 0.050306 | 7.35E-07 | |
z3 | 2 | 7 | 0.025936 | 0.00E+00 | 9 | 36 | 0.039643 | 2.35E-07 | |
z4 | 2 | 7 | 0.03822 | 0 | 9 | 35 | 0.041378 | 5.11E-07 | |
z5 | 2 | 7 | 0.03849 | 0 | 8 | 32 | 0.13231 | 1.24E-07 | |
z6 | 2 | 7 | 0.031354 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z7 | 101 | 404 | 3.4918 | 4.06E-09 | NaN | NaN | NaN | NaN | |
50000 | z1 | 2 | 7 | 0.091176 | 0 | 9 | 34 | 0.23565 | 0 |
z2 | 2 | 7 | 0.090561 | 0 | NaN | NaN | NaN | NaN | |
z3 | 2 | 7 | 0.13857 | 0.00E+00 | 9 | 35 | 0.12604 | 5.25E-07 | |
z4 | 2 | 7 | 0.10731 | 0.00E+00 | 10 | 38 | 0.426 | 0 | |
z5 | 2 | 7 | 0.14284 | 0.00E+00 | 8 | 31 | 0.47179 | 2.77E-07 | |
z6 | 2 | 7 | 0.29418 | 0.00E+00 | 9 | 35 | 0.21126 | 2.60E-07 | |
z7 | 110 | 439 | 8.6871 | 0 | 44 | 176 | 1.2526 | 3.55E-07 | |
100000 | z1 | 2 | 7 | 0.20371 | 0 | 9 | 36 | 0.2659 | 1.65E-07 |
z2 | 2 | 7 | 0.26727 | 0 | 8 | 30 | 0.48604 | 0 | |
z3 | 2 | 7 | 0.1588 | 0.00E+00 | 9 | 35 | 0.35032 | 7.42E-07 | |
z4 | 2 | 7 | 0.20624 | 0.00E+00 | 10 | 39 | 0.34301 | 1.62E-07 | |
z5 | 2 | 7 | 0.19404 | 0.00E+00 | NaN | NaN | NaN | NaN | |
z6 | 2 | 7 | 0.21718 | 0.00E+00 | 9 | 35 | 0.31142 | 3.68E-07 | |
z7 | 111 | 444 | 18.0039 | 6.11E-08 | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 34 | 127 | 0.026467 | 1.62E-07 | 71 | 263 | 0.16103 | 3.21E-07 |
z2 | 36 | 140 | 0.026972 | 7.43E-07 | 62 | 235 | 0.052281 | 1.13E-07 | |
z3 | 52 | 205 | 0.16096 | 2.58E-07 | 50 | 194 | 0.088863 | 3.72E-07 | |
z4 | 96 | 378 | 0.55079 | 4.35E-07 | NaN | NaN | NaN | NaN | |
z5 | 123 | 492 | 0.48012 | 3.96E-07 | NaN | NaN | NaN | NaN | |
z6 | 196 | 784 | 1.0967 | 6.21E-07 | NaN | NaN | NaN | NaN | |
z7 | 115 | 459 | 0.34961 | 2.89E-07 | NaN | NaN | NaN | NaN | |
5000 | z1 | 59 | 232 | 0.68163 | 2.32E-07 | 63 | 231 | 0.30231 | 3.90E-07 |
z2 | 50 | 188 | 0.29441 | 6.42E-07 | 72 | 282 | 0.18091 | 7.31E-07 | |
z3 | 179 | 709 | 2.2218 | 2.91E-07 | 60 | 232 | 0.14861 | 1.47E-07 | |
z4 | 171 | 684 | 2.9204 | 2.99E-07 | NaN | NaN | NaN | NaN | |
z5 | 297 | 1187 | 5.9983 | 3.31E-07 | NaN | NaN | NaN | NaN | |
z6 | 420 | 1680 | 9.6236 | 1.67E-07 | NaN | NaN | NaN | NaN | |
z7 | 187 | 744 | 3.4767 | 8.43E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 300 | 1.3784 | 1.39E-07 | 75 | 283 | 0.27114 | 2.35E-07 |
z2 | 74 | 283 | 1.5399 | 1.34E-07 | 55 | 208 | 0.20873 | 3.12E-07 | |
z3 | 214 | 843 | 5.0625 | 9.68E-07 | 67 | 259 | 0.65684 | 2.52E-07 | |
z4 | 253 | 1012 | 8.4598 | 5.48E-07 | NaN | NaN | NaN | NaN | |
z5 | 383 | 1531 | 15.2491 | 1.45E-07 | NaN | NaN | NaN | NaN | |
z6 | 575 | 2300 | 24.956 | 4.27E-07 | NaN | NaN | NaN | NaN | |
z7 | 323 | 1291 | 9.6152 | 2.90E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 135 | 534 | 12.3192 | 9.85E-07 | 65 | 253 | 1.9331 | 1.74E-07 |
z2 | 342 | 1357 | 46.7469 | 1.53E-07 | 94 | 369 | 4.3154 | 4.77E-07 | |
z3 | 326 | 1294 | 39.8986 | 4.97E-07 | NaN | NaN | NaN | NaN | |
z4 | 504 | 2016 | 82.9841 | 3.45E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | 602 | 2403 | 97.0953 | 6.65E-07 | NaN | NaN | NaN | NaN | |
100000 | z1 | 164 | 645 | 25.8558 | 1.87E-07 | NaN | NaN | NaN | NaN |
z2 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z3 | 400 | 1590 | 126.0758 | 7.38E-07 | NaN | NaN | NaN | NaN | |
z4 | 636 | 2544 | 240.5206 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z5 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z6 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | |
z7 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 9 | 36 | 0.17935 | 8.25E-07 | 9 | 36 | 0.0153 | 8.24E-07 |
z2 | 9 | 36 | 0.03051 | 7.93E-07 | 9 | 36 | 0.048509 | 7.93E-07 | |
z3 | 9 | 36 | 0.027967 | 6.99E-07 | 9 | 36 | 0.017521 | 6.98E-07 | |
z4 | 9 | 36 | 0.015472 | 4.79E-07 | 9 | 36 | 0.014811 | 4.78E-07 | |
z5 | 9 | 36 | 0.007122 | 3.84E-07 | 9 | 36 | 0.016431 | 3.83E-07 | |
z6 | 9 | 36 | 0.010164 | 2.27E-07 | 9 | 36 | 0.009737 | 2.26E-07 | |
z7 | 9 | 36 | 0.020191 | 7.23E-07 | 9 | 36 | 0.017515 | 7.06E-07 | |
5000 | z1 | 10 | 40 | 0.048118 | 1.85E-07 | 10 | 40 | 0.082844 | 1.85E-07 |
z2 | 10 | 40 | 0.097072 | 1.78E-07 | 10 | 40 | 0.050343 | 1.78E-07 | |
z3 | 10 | 40 | 0.032297 | 1.57E-07 | 10 | 40 | 0.10792 | 1.57E-07 | |
z4 | 10 | 40 | 0.043942 | 1.07E-07 | 10 | 40 | 0.076199 | 1.07E-07 | |
z5 | 9 | 36 | 0.043841 | 8.61E-07 | 9 | 36 | 0.037916 | 8.61E-07 | |
z6 | 9 | 36 | 0.033263 | 5.08E-07 | 9 | 36 | 0.069375 | 5.08E-07 | |
z7 | 10 | 40 | 0.037194 | 1.58E-07 | 10 | 40 | 0.047672 | 1.58E-07 | |
10000 | z1 | 10 | 40 | 0.082406 | 2.62E-07 | 10 | 40 | 0.076648 | 2.62E-07 |
z2 | 10 | 40 | 0.068947 | 2.52E-07 | 10 | 40 | 0.15678 | 2.52E-07 | |
z3 | 10 | 40 | 0.058721 | 2.22E-07 | 10 | 40 | 0.13597 | 2.22E-07 | |
z4 | 10 | 40 | 0.078257 | 1.52E-07 | 10 | 40 | 0.08399 | 1.52E-07 | |
z5 | 10 | 40 | 0.062069 | 1.22E-07 | 10 | 40 | 0.07822 | 1.22E-07 | |
z6 | 9 | 36 | 0.053275 | 7.18E-07 | 9 | 36 | 0.1205 | 7.18E-07 | |
z7 | 10 | 40 | 0.057688 | 2.24E-07 | 10 | 40 | 0.080168 | 2.23E-07 | |
50000 | z1 | 10 | 40 | 0.22352 | 5.85E-07 | 10 | 39 | 0.38243 | 5.85E-07 |
z2 | 10 | 40 | 0.27436 | 5.63E-07 | 10 | 39 | 0.41361 | 5.63E-07 | |
z3 | 10 | 40 | 0.23122 | 4.96E-07 | 10 | 39 | 0.30721 | 4.96E-07 | |
z4 | 10 | 40 | 0.21192 | 3.40E-07 | 10 | 39 | 0.43086 | 3.40E-07 | |
z5 | 10 | 40 | 0.23892 | 2.72E-07 | 10 | 38 | 0.29829 | 1.26E-15 | |
z6 | 10 | 40 | 0.29017 | 1.61E-07 | 10 | 38 | 0.51415 | 6.28E-16 | |
z7 | 10 | 40 | 0.25616 | 5.01E-07 | 10 | 39 | 0.29756 | 5.00E-07 | |
100000 | z1 | 10 | 40 | 0.82944 | 8.28E-07 | 10 | 39 | 1.1183 | 8.28E-07 |
z2 | 10 | 40 | 0.47168 | 7.96E-07 | 10 | 38 | 0.6117 | 6.28E-16 | |
z3 | 10 | 40 | 0.49749 | 7.01E-07 | 10 | 38 | 0.81145 | 6.28E-16 | |
z4 | 10 | 40 | 0.52125 | 4.80E-07 | 10 | 38 | 0.79886 | 0 | |
z5 | 10 | 40 | 0.69499 | 3.85E-07 | 10 | 38 | 0.60219 | 0 | |
z6 | 10 | 40 | 0.47656 | 2.27E-07 | 10 | 38 | 0.72864 | 0 | |
z7 | 10 | 40 | 0.49578 | 7.07E-07 | 10 | 39 | 0.80741 | 7.07E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 5 | 20 | 0.046544 | 3.24E-07 | 5 | 20 | 0.008647 | 3.24E-07 |
z2 | 5 | 20 | 0.009418 | 1.43E-07 | 5 | 20 | 0.013849 | 1.43E-07 | |
z3 | 5 | 20 | 0.038932 | 1.68E-08 | 4 | 16 | 0.015388 | 5.81E-08 | |
z4 | 6 | 24 | 0.01166 | 9.16E-09 | 6 | 24 | 0.010967 | 3.39E-08 | |
z5 | 6 | 24 | 0.010929 | 1.23E-08 | 6 | 24 | 0.0107 | 4.99E-08 | |
z6 | 6 | 23 | 0.01937 | 1.04E-07 | 6 | 23 | 0.014025 | 6.55E-08 | |
z7 | 26 | 104 | 0.032336 | 8.36E-09 | 36 | 144 | 0.12555 | 5.34E-08 | |
5000 | z1 | 5 | 20 | 0.029586 | 7.25E-07 | 5 | 20 | 0.041107 | 7.25E-07 |
z2 | 5 | 20 | 0.027892 | 3.20E-07 | 5 | 20 | 0.038182 | 3.20E-07 | |
z3 | 5 | 20 | 0.035333 | 3.75E-08 | 4 | 16 | 0.12123 | 1.30E-07 | |
z4 | 6 | 24 | 0.032225 | 2.05E-08 | 6 | 24 | 0.05211 | 7.58E-08 | |
z5 | 6 | 24 | 0.026546 | 2.75E-08 | 6 | 24 | 0.038675 | 1.12E-07 | |
z6 | 6 | 23 | 0.032529 | 2.32E-07 | 6 | 23 | 0.081384 | 1.46E-07 | |
z7 | 34 | 136 | 0.24122 | 3.59E-08 | 41 | 164 | 0.29917 | 1.14E-07 | |
10000 | z1 | 6 | 24 | 0.043879 | 5.12E-09 | 6 | 24 | 0.079589 | 5.12E-09 |
z2 | 5 | 20 | 0.036531 | 4.52E-07 | 5 | 20 | 0.1417 | 4.52E-07 | |
z3 | 5 | 20 | 0.050902 | 5.31E-08 | 4 | 16 | 0.045901 | 1.84E-07 | |
z4 | 6 | 24 | 0.054078 | 2.90E-08 | 6 | 24 | 0.059807 | 1.07E-07 | |
z5 | 6 | 24 | 0.052048 | 3.89E-08 | 6 | 24 | 0.099213 | 1.58E-07 | |
z6 | 6 | 23 | 0.04894 | 3.28E-07 | 6 | 23 | 0.054029 | 2.07E-07 | |
z7 | 41 | 164 | 0.30793 | 3.45E-08 | 45 | 180 | 0.92444 | 3.64E-07 | |
50000 | z1 | 6 | 24 | 0.14 | 1.15E-08 | 6 | 24 | 0.26027 | 1.15E-08 |
z2 | 6 | 24 | 0.14343 | 5.06E-09 | 6 | 24 | 0.60276 | 5.06E-09 | |
z3 | 5 | 20 | 0.15201 | 1.19E-07 | 4 | 16 | 0.17247 | 4.11E-07 | |
z4 | 6 | 24 | 0.34794 | 6.48E-08 | 6 | 24 | 0.22999 | 2.40E-07 | |
z5 | 6 | 24 | 0.15433 | 8.70E-08 | 6 | 24 | 0.38048 | 3.53E-07 | |
z6 | 6 | 23 | 0.1425 | 7.35E-07 | 6 | 23 | 0.2271 | 4.63E-07 | |
z7 | 29 | 116 | 1.295 | 9.41E-09 | 44 | 176 | 2.2436 | 7.06E-07 | |
100000 | z1 | 6 | 24 | 0.39791 | 1.62E-08 | 6 | 24 | 0.94834 | 1.62E-08 |
z2 | 6 | 24 | 0.47548 | 7.15E-09 | 6 | 24 | 0.43453 | 7.15E-09 | |
z3 | 5 | 20 | 0.48174 | 1.68E-07 | 4 | 16 | 0.29517 | 5.81E-07 | |
z4 | 6 | 24 | 0.26721 | 9.16E-08 | 6 | 24 | 0.55119 | 3.39E-07 | |
z5 | 6 | 24 | 0.28512 | 1.23E-07 | 6 | 24 | 0.61073 | 4.99E-07 | |
z6 | 7 | 27 | 0.5385 | 5.19E-09 | 6 | 23 | 0.42035 | 6.55E-07 | |
z7 | 29 | 116 | 1.6021 | 1.19E-08 | 41 | 164 | 3.9953 | 9.23E-07 |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 66 | 264 | 0.934 | 3.48E-07 | NaN | NaN | NaN | NaN |
z2 | 101 | 404 | 0.99428 | 4.28E-07 | 41 | 164 | 0.75214 | 4.29E-07 | |
z3 | 40 | 160 | 0.40127 | 3.33E-07 | NaN | NaN | NaN | NaN | |
z4 | 39 | 156 | 0.5071 | 5.07E-07 | 39 | 156 | 0.71207 | 3.83E-07 | |
z5 | 36 | 144 | 0.61923 | 4.69E-07 | 35 | 140 | 1.4123 | 4.07E-07 | |
z6 | 4 | 14 | 0.071864 | NaN | 4 | 14 | 0.059454 | NaN | |
z7 | 23 | 89 | 0.48051 | NaN | NaN | NaN | NaN | NaN | |
5000 | z1 | 52 | 208 | 2.7649 | 2.91E-07 | NaN | NaN | NaN | NaN |
z2 | 44 | 176 | 2.1027 | 3.54E-07 | NaN | NaN | NaN | NaN | |
z3 | 42 | 168 | 2.1325 | 2.95E-07 | NaN | NaN | NaN | NaN | |
z4 | 37 | 148 | 2.0738 | 3.41E-07 | NaN | NaN | NaN | NaN | |
z5 | 16 | 60 | 0.64982 | NaN | NaN | NaN | NaN | NaN | |
z6 | 20 | 76 | 0.98188 | NaN | NaN | NaN | NaN | NaN | |
z7 | 301 | 1202 | 18.7543 | 4.37E-07 | NaN | NaN | NaN | NaN | |
10000 | z1 | 77 | 303 | 9.6495 | 3.64E-07 | NaN | NaN | NaN | NaN |
z2 | 71 | 284 | 8.0859 | 3.74E-07 | NaN | NaN | NaN | NaN | |
z3 | 62 | 248 | 7.1755 | 3.27E-07 | NaN | NaN | NaN | NaN | |
z4 | 48 | 192 | 4.1575 | 4.42E-07 | NaN | NaN | NaN | NaN | |
z5 | 15 | 55 | 0.93456 | NaN | NaN | NaN | NaN | NaN | |
z6 | 123 | 490 | 12.4072 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z7 | 307 | 1226 | 35.579 | 3.46E-07 | NaN | NaN | NaN | NaN | |
50000 | z1 | 24 | 89 | 8.5017 | NaN | NaN | NaN | NaN | NaN |
z2 | 89 | 355 | 45.0395 | 4.34E-07 | NaN | NaN | NaN | NaN | |
z3 | 65 | 260 | 28.4752 | 3.57E-07 | NaN | NaN | NaN | NaN | |
z4 | 431 | 1718 | 135.7493 | 3.88E-07 | NaN | NaN | NaN | NaN | |
z5 | 6 | 21 | 2.1067 | NaN | NaN | NaN | NaN | NaN | |
z6 | 6 | 21 | 1.8349 | NaN | NaN | NaN | NaN | NaN | |
z7 | 7 | 24 | 1.8872 | NaN | NaN | NaN | NaN | NaN | |
100000 | z1 | 34 | 130 | 31.5135 | NaN | NaN | NaN | NaN | NaN |
z2 | 5 | 17 | 1.9076 | NaN | NaN | NaN | NaN | NaN | |
z3 | 87 | 332 | 64.5816 | 3.00E-07 | NaN | NaN | NaN | NaN | |
z4 | 76 | 303 | 68.3533 | 4.49E-07 | NaN | NaN | NaN | NaN | |
z5 | 5 | 17 | 2.2305 | NaN | NaN | NaN | NaN | NaN | |
z6 | 5 | 17 | 2.5293 | NaN | NaN | NaN | NaN | NaN | |
z7 | 6 | 21 | 3.1078 | NaN | NaN | NaN | NaN | NaN |
Algo.1 | Algo.2 | ||||||||
dim | inp | nit | nfv | tim | norm | nit | nfv | tim | norm |
1000 | z1 | 10 | 34 | 0.032445 | 1.06E-07 | 10 | 34 | 0.005932 | 1.06E-07 |
z2 | 10 | 34 | 0.008239 | 1.06E-07 | 10 | 34 | 0.010335 | 1.06E-07 | |
z3 | 10 | 34 | 0.0073 | 1.06E-07 | 10 | 34 | 0.008407 | 1.06E-07 | |
z4 | 10 | 34 | 0.008495 | 1.06E-07 | 10 | 34 | 0.010614 | 1.06E-07 | |
z5 | 10 | 34 | 0.00772 | 1.06E-07 | 10 | 34 | 0.00775 | 1.06E-07 | |
z6 | 10 | 34 | 0.011383 | 1.06E-07 | 10 | 35 | 0.009311 | 1.06E-07 | |
z7 | 67 | 213 | 0.024778 | 9.71E-07 | 10 | 34 | 0.008864 | 1.06E-07 | |
5000 | z1 | 7 | 25 | 0.022534 | 6.89E-08 | 7 | 25 | 0.027033 | 6.89E-08 |
z2 | 7 | 25 | 0.032305 | 6.89E-08 | 7 | 25 | 0.02838 | 6.89E-08 | |
z3 | 7 | 25 | 0.026468 | 6.89E-08 | 7 | 25 | 0.068469 | 6.89E-08 | |
z4 | 7 | 25 | 0.034453 | 6.89E-08 | 7 | 26 | 0.037886 | 6.89E-08 | |
z5 | 7 | 25 | 0.021703 | 6.89E-08 | 7 | 26 | 0.037186 | 6.89E-08 | |
z6 | 7 | 25 | 0.027352 | 6.89E-08 | 7 | 26 | 0.077955 | 6.89E-08 | |
z7 | 20 | 66 | 0.061189 | 9.72E-07 | 7 | 25 | 0.037992 | 6.89E-08 | |
10000 | z1 | 6 | 22 | 0.07498 | 8.13E-08 | 6 | 22 | 0.054682 | 8.13E-08 |
z2 | 6 | 22 | 0.047478 | 8.13E-08 | 6 | 22 | 0.21797 | 8.13E-08 | |
z3 | 6 | 22 | 0.052347 | 8.13E-08 | 6 | 22 | 0.081579 | 8.13E-08 | |
z4 | 6 | 22 | 0.047644 | 8.13E-08 | 6 | 23 | 0.085064 | 8.13E-08 | |
z5 | 6 | 22 | 0.068304 | 8.13E-08 | 6 | 23 | 0.19028 | 8.13E-08 | |
z6 | 6 | 22 | 0.042771 | 8.13E-08 | 6 | 23 | 0.15365 | 8.13E-08 | |
z7 | 12 | 41 | 0.074071 | 9.08E-07 | 6 | 22 | 0.056989 | 8.13E-08 | |
50000 | z1 | 5 | 19 | 0.22112 | 1.41E-07 | 5 | 19 | 0.60662 | 1.41E-07 |
z2 | 5 | 19 | 0.21638 | 1.41E-07 | 5 | 19 | 0.33244 | 1.41E-07 | |
z3 | 5 | 19 | 0.22186 | 1.41E-07 | 5 | 20 | 0.8389 | 1.41E-07 | |
z4 | 5 | 19 | 0.37207 | 1.41E-07 | 5 | 20 | 0.63139 | 1.41E-07 | |
z5 | 5 | 19 | 0.36107 | 1.41E-07 | 5 | 20 | 1.046 | 1.41E-07 | |
z6 | 5 | 19 | 0.27063 | 1.41E-07 | 5 | 20 | 1.4673 | 1.41E-07 | |
z7 | 59 | 235 | 2.7862 | 4.11E-07 | 5 | 19 | 0.57234 | 1.41E-07 | |
100000 | z1 | 6 | 23 | 0.93893 | 2.10E-07 | 6 | 23 | 1.3525 | 2.10E-07 |
z2 | 6 | 23 | 0.60445 | 2.10E-07 | 6 | 24 | 1.5313 | 2.10E-07 | |
z3 | 6 | 23 | 0.71683 | 2.10E-07 | 6 | 24 | 1.6022 | 2.10E-07 | |
z4 | 6 | 23 | 0.57114 | 2.10E-07 | 6 | 24 | 1.7882 | 2.10E-07 | |
z5 | 6 | 23 | 0.57099 | 2.10E-07 | 6 | 24 | 1.878 | 2.10E-07 | |
z6 | 6 | 23 | 0.69104 | 2.10E-07 | 6 | 24 | 1.9634 | 2.10E-07 | |
z7 | 34 | 135 | 4.3899 | 4.52E-07 | 6 | 23 | 1.4688 | 2.10E-07 |