The details of the folding mechanisms have not yet been fully understood for many proteins, and it is believed that the information on the folding mechanism of a protein is encoded in its amino acid sequence. β-trefoil proteins are known to have the same 3D scaffold, namely, a three-fold symmetric scaffold, despite the proteins’ low sequence identity among superfamilies. In this study, we extract an initial folding unit from the amino acid sequences of irregular β-trefoil proteins by constructing an average distance map (ADM) and utilizing inter-residue average distance statistics to determine the relative contact frequencies for residue pairs in terms of F values. We compare our sequence-based prediction results with the packing between hydrophobic residues in native 3D structures and a Gō-model simulation.The ADM and F-value analyses predict that the N-terminal and C-terminal regions are compact and that the hydrophobic residues at the central region can be regarded as an interaction center with other residues. These results correspond well to those of the Gō-model simulations. Moreover, our results indicate that the irregular parts in the β-trefoil proteins do not hinder the protein formation. Conserved hydrophobic residues on the β5 strand are always the interaction center of packing between the conserved hydrophobic residues in both regular and irregular β-trefoil proteins.We revealed that the β5 strand plays an important role in β-trefoil protein structure construction. The sequence-based methods used in this study can extract the protein folding information from only amino acid sequence data, and well corresponded to 3D structure-based Gō-model simulation and available experimental results. A β-trefoil protein exhibits pseudo three-fold symmetry and is observed widely in the protein 3D structure space. We show the 3D structure and schematic drawings of the three symmetrical units of cytokine (2K8R) as a representative β-trefoil protein in Fig. In the present study, we investigate the relationship between the folding mechanisms of β-trefoil proteins with irregular structures and their amino acid sequences. We utilize the same techniques as in our previous study,  in whichWe also focus on the hydrophobic packing formed by conserved hydrophobic residues in the native structures and compare the packing hydrophobic residues and the residues significant in folding. To confirm the results that we predict from the amino acid sequence information, we conduct Gō-model simulations. From the results obtained, we identify the residues significant for irregular β-trefoil proteins to fold into the 3D structures.In the present study, we apply the coarse-grained Gō model which we have developed –15. Thishttps://www.rcsb.org/) [Clostridium sp. While 1TTU was detected in transparent nematode, Caenorhabditis elegans, which classified as a part of CSL protein and associated with cell to cell communication. These four 3D structures are illustrated in Fig. In our previous study, we examined regularly structured single-domain proteins of up to 180 residues. That is, we excluded proteins in the STI-like, DNA-binding protein LAG-1 (CSL), and Agglutinin superfamilies. In this study, we selected trefoil proteins containing approximately 180 residues with irregular structures (due to insertion or deletion) from either the STI-like superfamily and the DNA-binding protein LAG-1 (CSL) superfamily: Tetanus toxin (PDB ID (sb.org/) : 1A8D), sb.org/) –28. The An average distance map (ADM) is a kind of predicted contact map constructed from the inter-residue average distance statistics, which is created using only the amino acid sequence information of a protein. This method was originally developed to predict the location of structural domains in a protein . The metThe inter-residue average distance for a pair of residues refers to the inter-Cα atomic distance between these residues. Every pair of amino acid type were considered in the calculations of the inter-residue average distances. The separation of the two residues along the amino acid sequence of a protein was considered in calculating the average distance of a residue pair. This separation is called the “range”. The ranges are defined as follows: M = 1 when 1 ≤ k ≤ 8, M = 2 when 9 ≤ k ≤ 20, M = 3 when 21 ≤ k ≤ 30, M = 4 when 31 ≤ k ≤ 40, and so on, where k = |i - j| and M is a range. That is, in each range, the average distances for all pairs of all amino acid types were calculated. Let d be the average distance of amino acid types A and B in the range M.t, P(M)c, and D are the total number of residue pairs with statistically significant average distances, [c is the number of residue pairs with statistically significant average distances smaller than the cutoff distance for M, and D is an adjustable parameter that provides the average plot density of the corresponding ADM close to that of the contact map constructed based on the spatial distances calculated from the actual 3D structure of a protein , respectively. The average plot density is approximated by the following formula: [When d is less than the cutoff distance previously determined for the range M, a plot is made on the map. The set of cutoff distances for the ranges is defined by the following equation:stances,  P(M)c isformula: .2\documρav when we use C = 36.12 [c. Thus, a map is derived from only the amino acid sequence of a protein based on the inter-residue average distance statistics.Here, N is the total number of residues in a protein and C is the constant value derived from our previous study . The plo = 36.12 . To cons∆ρi are estimated from residue 1 to the total number of residues in a given protein. The plots obtained by the line parallel to the x-axis are called vertical scanning, and those obtained by the line parallel to the y-axis is called horizontal scanning. The v of With the constructed ADM for a given protein, a compact region in the protein is predicted as follows. First, the plot density differences in the map are calculated. A density difference means the difference in plot density values between the triangular and trapezoidal parts of the ADM, The detection of a compact region’s boundaries is made based on s of m-p .A region with a high density of plots, with a high ƞ value, is regarded as a predicted compact region in a 3D structure. We also regard the predicted region as compact in the early stage of folding.Multiple sequence alignment provides valuable information about many protein characteristics, including conserved regions which might be related to 3D structure or functional property.In general, the sequence identities of β-trefoil proteins from different superfamilies are relatively low, making accurate multiple alignments based on only sequences difficult. To detect the relationships among sequences with relatively low sequence identity, this study utilized a multiple sequence alignment technique using secondary structure information, the Combinatorial Extension  program Sequence conservation is provided by evolutionary pressure to maintain a given structure and/or structure functions , 33. In The similarity of the location of the predicted compact regions can be regarded as conservation of the predicted compact regions during molecular evolution. A multiple sequence alignment is used to define the conservation of the regions predicted by the ADMs. The procedure is as follows.The number of residues at a given site that are commonly included in the predicted compact regions is counted to calculate the conserved ratio . We then make a histogram of this ratio versus the site number. A region covering several residues with high ratios denotes a conserved predicted compact region during evolution. Currently, the predicted compact regions are regarded as being conserved when the conservation ratios exceed 70% in the same position of the aligned samples .i,j derived from average distance ¯ri,j and its standard deviation σi,j, was employed in a simulation of protein conformations. The bond and dihedral angles of the initial conformation were randomly selected. During a simulation, the bond and dihedral angles between the residue i and i + 1 are bent and rotated randomly. That is, a simulation is performed starting from a totally random distribution and the restrictions derived from the average distance statistics. The alteration of all the bond and dihedral angles is included in one MC step followed by the Metropolis judgment. We made an assumption that density of the potential between two residues, An effective inter-residue potential can be derived from the present inter-residue average distance statistics. In order to analyze the initial folding process of a protein, we performed conformational sampling of a protein in a random state, that is, no secondary or tertiary structure formed, with this potential to identify a residue where initial folding events, such as hydrophobic collapse, occurs . A modelwhere this equation is expressed by Eq. We obtain Eqs. where kT is set so that the MC acceptance ratio is 0.5. The obtained potential is a harmonic potential to reproduce average distances and standard deviations in the statistics. The significant value in a calculation is the difference between the energy values of conformations, and Z does not appear in the calculation explicitly. Thus, we ignored Z in the calculations.It is expected that ensembles with reproducible inter-residue average distance statistics using this potential can be obtained. The contact frequency, g, for each pair of residues is estimated with structures generated from a simulation using the potential energy function. Then the residue contact frequency, g, in the same range M is normalized, that is, the value corresponding to the z-value in statistical theory. We refer this value as Q. Here, D(M) is the standard deviation of the contact frequency g with two residues separated in range M. These are expressed by Eq. where i and j are the residue numbers.i, by summing the normalized contact frequencies, Q, from j = 1 to N for each residue i, where N is the total number of residues:Finally, we obtain the relative contact frequency, Fi the “F value”. Residues at the peaks in the plot of F values are expected to be located in the center of many inter-residue contacts, such as a hydrophobic cluster. A region near a peak (within ± 5 residues) [Fcut) as presented in Eq. We call the value Fesidues)  of an F-i is the F value of residue i and N is the total residue number, this residue is defined as a peak.where FIt has been confirmed for several proteins –8, 12 thA Gō model technique has been applied widely to the folding simulation of a protein –15, 34. The potential energy of a structure Γ is defined by Eq. ij, NC, and NNC indicate the bond angle, dihedral angle, inter-residue distance, native contacts, and non-native contacts, respectively. The subscript 0 refers to the values related to the native structure. We use the parameters, Kθ = 20ε, ij corresponds to the number of inter-heavy atom contacts divided by the average number of inter-heavy atom contacts per residue pair; it indicates the strength of the scaled inter-residue interactions. Bij (Θij), which is defined by Eqs. The first, second, third, and fourth terms correspond to the energies of the bond angle, dihedral angle, native interactions, and non-native interactions, respectively. θ, ϕ, r + 1.4 Å . The locmentclasspt{minimaij indicates the relative orientation of the side chains of the i-th and j-th residues implicitly, namely, the relative angle between hi and hj. hi is defined as ri, i − 1 + ri, i + 1, and ri, i − 1 denotes a vector between the i-th and (i - 1) th residues. hi is used to define a bond vector mimicking the Cβ-Cα vector in the combination of ri, i − 1 × ri, i + 1 [ij is close to the native value, Bij ~ 1, the residues make a contact. When Θij exceeds a cutoff value, Bij ~ 0, the residues cannot make a contact. A cutoff value aΘ = 0.6π was used [Bij = 1 because we cannot define the vector hi. We keep θ < π to prevent hi = 0.Θi, i + 1 . When Θiwas used . For theA replica exchange MC simulation was used in the present study . M iteraIn this study, an order parameter indicating the closeness of a sampled structure to the native structure of a protein is defined by the following equation.The structural features of sampled structures with a specific Q are expressed using a contact frequency map. A contact frequency map is constructed by plotting the contact frequencies of various pairs of residues on a contact map. Thus, a contact frequency map shows the features of an intermediate state during folding.Figure The result of the ADM analysis of 1A8D is shown in Fig. The peaks of the F-value plot appear near β5-β6 and β7 as shown in Fig. Figure Figure As is common with the proteins in the STI-like superfamily, the ADM predicted regions at N-terminus and C-terminus correspond well to the N-terminal and C-terminal trefoil units in each of the three proteins. The results of the present study show a remarkable correspondence of the ADM predicted regions at the N-terminus and C-terminus with those predicted in the previous study . As mentFigure Next, we analyze the hydrophobic packing among CHRs in a protein based on its 3D structure. In particular, we analyze how CHRs near the peaks of the F-value plot form hydrophobic packing in the native structure of a protein. First of all, three proteins in the STI-like superfamily are treated. Figure The F-value plot for 1EPW shows the highest peak at a residue in β5. Figure In the 3D structure of 3BTA, CHR-β5C interacts with CHR-β4N and CHR-β4C in the predicted region-2, as shown in Fig. There are 26 common contacts formed by CHRs in three proteins of the STI-like superfamily. Figure In the case of 1TTU, as shown in Fig. Let us compare the hydrophobic packing in the symmetric β-trefoil proteins with that in the proteins with irregular structures Fig. b. The coIt is interesting to see the interaction between CHR-β6 and CHR-β7 conserved in 26 β-trefoil proteins with the high symmetry structures and three STI-like superfamily proteins. However, this packing disappears in 1TTU because β7 is missing. Instead of this packing, a new interaction between CHR-β6 and CHR-β10 is observed. It is thought that this interaction between CHR-β6 and CHR-β10 in 1TTU compensates for the missing interaction between CHR-β6 and CHR-β8.In this section, we present the results of the Gō-model simulations. Figure Next, we present the result of Gō-model simulation for 1A8D. In Fig. The second transition state presents at Q = 0.4. From the observation of the contacts at Q = 0.4, the CHRs in trefoil unit-2 tend to form contacts with the CHRs in trefoil unit-1 and unit-3 rather than within trefoil unit-2.In the present study, the folding initiation sites in the β-trefoil proteins with irregular structures were predicted from their amino acid sequences and further analyses were made regarding the packing formed by CHRs based on the 3D structures. These results were verified by Gō-model simulations. As a result, CHRs in the central trefoil unit with high F-value peaks interact with CHRs within the trefoil unit and with CHRs in other trefoil units, followed by the stabilization and structural formation of ADM-predicted regions corresponding to the N-terminal and C-terminal trefoil units. For example, in the folding of 1A8D, the hydrophobic packing formed by CHRs in the ADM-predicted region-1 (β1-β4) and region-3 (β10-β12) play significant roles in forming the N-terminal and C-terminal units, respectively, as indicated in Fig. These facts suggest that the information about the initial stage of folding of a protein can be extracted from its sequence by ADMs and F-value analyses. A Gō-model simulation in the present study demonstrates that CHRs that form contacts are mainly within an ADM-predicted region in the early stage of folding. These CHRs are located around F-value peaks. Contacts by CHRs between ADM-predicted regions start to form with increasing Q value, as is the case for 1A8D in Fig. As an attempt, we perform the predictions of disordered regions based on our new technique . The resIn this study, the common 14 contacts formed by CHRs in the β-trefoil proteins with high symmetry could be defined. According to this result, 11 of the 14 common contacts are also observed in the β-trefoil proteins with irregular structures. Thus, these 11 contacts seem to be especially significant in the formation of the β-trefoil scaffold. Two of four deficient contacts, namely, the contacts between β6 and β7 and between β7 and β10, are caused by the deficiency of β7 in 1TTU. The corresponding contacts are observed in the other three proteins, that is, 1A8D, 1EPW, and 3BTA. These corresponding contacts seem to be significant but not indispensable for β-trefoil structure formation. The other contact between β6 and β8 is not observed in 3BTA and 1TTU. It should be noted that the residues corresponding to this contact pair are close to each other in 3BTA. In 1TTU, these corresponding two residues are located within three residues along the sequence. Therefore, we do not take these two residues into account.In the three STI-like superfamily proteins, the ADM-predicted regions always contain the insertion parts, suggesting that this insertion does not disturb the N-terminal trefoil-unit formation. In the Gō-model simulations, some contacts formed by the residues in the insertion part are observed in the early stage of folding (Q = 0.2).The native contacts in 1TTU show that β6 interacts with β10 in the C-terminal side Fig. . This coIn the present study, the results from Gō-model simulations coincide well with the predictions made by the ADMs and F-value analyses based on the amino acid sequence information. ADMs and F-value analyses can decode the folding information from the amino acid sequences of not only the β-trefoil proteins with high symmetry but also of those with irregular structures.Finally, we mention that we are currently thinking to make a webserver to perform present analyses for various proteins in near future.The present study demonstrates that the ADM-predicted regions in the N-terminal and C-terminal parts correspond well to the N-terminal and C-terminal β-trefoil units of a β-trefoil protein with an irregular structure. The insertion part is always in the N-terminal ADM-predicted region for each of the three proteins in the STI-like superfamily. In contrast, a loop region tends to be excluded from an ADM-predicted region for a highly symmetrical β-trefoil protein . These fThe property of the peak(s) of the F-value plot for a highly symmetrical β-trefoil protein appearing in the central region is also observed for a β-trefoil protein with an irregular structure. Thus, this property is quite common in the space of β-trefoil protein 3D structures.The analyses of the packing formed by CHRs in the native structures reveal 11 common interactions, which are considered to be significant factors in constructing the β-trefoil scaffold. In particular, we revealed the central role of CHR-β5N and CHR-β5C in forming both symmetric and irregular β-trefoil scaffolds.Thus, our results suggest that the folding properties of highly symmetrical and irregular β-trefoil proteins are basically conserved, and our sequence-based techniques can decode these properties from their amino acid sequences.Additional file 1.


Many previous clinical studies have found that accumulated sequential mutations are statistically related to tumorigenesis. However, they are limited in fully elucidating the significance of the ordered-mutation because they did not focus on the network dynamics. Therefore, there is a pressing need to investigate the dynamics characteristics induced by ordered-mutations.To quantify the ordered-mutation-inducing dynamics, we defined the mutation-sensitivity and the order-specificity that represent if the network is sensitive against a double knockout mutation and if mutation-sensitivity is specific to the mutation order, respectively, using a Boolean network model.Through intensive investigations, we found that a signaling network is more sensitive when a double-mutation occurs in the direction order inducing a longer path and a smaller number of paths than in the reverse order. In addition, feedback loops involving a gene pair decreased both the mutation-sensitivity and the order-specificity. Next, we investigated relationships of functionally important genes with ordered-mutation-inducing dynamics. The network is more sensitive to mutations subject to drug-targets, whereas it is less specific to the mutation order. Both the sensitivity and specificity are increased when different-drug-targeted genes are mutated. Further, we found that tumor suppressors can efficiently suppress the amplification of oncogenes when the former are mutated earlier than the latter.Taken together, our results help to understand the importance of the order of mutations with respect to the dynamical effects in complex biological systems. Myeloproliferative Neoplasms that JAK2 mutation followed by TET2 mutation influenced the clinical features  ∈ {0, 1}N. Every network state transits to another network state determined by a set of Boolean update functions F = {f1, f2, …, fN} which is synchronously updated f1, f2, …fN, and f1, f2, …fN eventually converges to either a fixed point or a limit-cycle attractor. The attractor is rigorously defined as follows.A Definition. Let v(0), v(1), ⋯v(t), ⋯ be a network state trajectory starting at v(0). Then, the attractor denoted by 〈G, F, v(0)〉 is represented by an ordered finite sub-list of the trajectory, , where τ is the smallest time-step such that v(t) = v(t + p) for ∀t ≥ τ with v(i) ≠ v(j) for ∀ i ≠ j ∈ {τ, τ + 1, …, τ + p − 1}. Herein, p is called the attractor length.t is found such that v(t) = v(t + p).To identify an attractor, the network state trajectory is computed by synchronously updating the state values of all nodes until the time-step G with a set of nodes V = {v1, v2, …, vN} specified by a set of corresponding update-rules F = {f1, f2, …, fN}, consider a state trajectory starting from an arbitrary initial state. When a network is subject to a mutation, the trajectory may converge to a different attractor. Then, the network is regarded as sensitive to the mutation. Let W ⊆ V be a set of genes subject to knockout mutations [FW as a set of update-rules where every gene in W ⊆ V is frozen to 0 (off state) in F. In this work, we investigate the effect of the ordered double-mutations on the network dynamics. Let  be an ordered pair of nodes subject to a double-mutation with a time gap T, which means that vk is first mutated at time-step t = 0, and then vl is mutated at time-step t = T. In other words, the time gap represents the time-step lag between the occurrences of the first and the second mutation. We can implement it by assuming that t < T and t ≥ T, respectively. It has been known that the notion of the time gap is important since it can affect the mutation process [vk, vl)-ordered double-mutation, we can define the mutation-sensitivity as follows:S is a set of considered initial-states and I(condition) denotes an indicator function that returns 1 if the condition is true and 0, otherwise. In other words, δ represents the probability that a network converges to a different attractor by the double knockout mutation. To quantify the specificity of dynamics with respect to the mutation order, we define the order-specificity as follows:Given a Boolean network utations , 42, and process , 43, 44.v3, v4} be a pair of genes subject to mutations and 0100 be a given initial state. Then, a wild-type attractor denoted by Att1 is computed by applying F all the time. Next, we compute Att2 and Att3 to which the network converges against - and -ordered mutations, respectively. Note that t < T and t ≥ T, respectively, in computing Att2 (resp. Att3). When Att2 (or Att3) is not identical to Att1, the network is regarded as sensitive to the -ordered -ordered) mutation. In addition, the network dynamics are specific to the mutation order if Att2 and Att3 are not identical to each other. We note that a pair of genes  with a common child node in the network are excluded from analysis in this study. In case that there exists such a common child node vc, it is probable that the update of vc is differently affected by the -ordered and the -ordered mutations, because the occurrence order of vk and vl in the NCF to update vc represents the degree of influence on the update of vc. Finally, we note that the network dynamics can depend on the initial network states. Therefore, a total of 1000 initial-states  were randomly generated to compute the mutation-sensitivity and the order-specificity values in Eqs. (1) and (2) in all simulations of this study.In other words, Δ represents the probability of a network converging to different attractors by different mutation orders. Figure vi, vj) denoted by l is defined by the number of links included in the shortest path from vi and vj.The path length of  denoted by n is defined by the number of non-identical paths from vi and vj.The number of paths of (A feedback loop (FBL) is a sequence of nodes where no node is repeated except the starting and the ending nodes. It has been known that FBLs play an important role in controlling dynamics behaviors of cellular signaling networks , 46, 47.Some structural characteristics of genes are related to network dynamic stability . In thisTo verify that the results of mutation-sensitivity and order-specificity in the real molecular interaction networks are consistent with randomly structured networks, we generated random networks using the Barabási Albert (BA)  model whin-silico simulations, we basically implemented the program code using PANET [For efficient ng PANET  which isIn this paper, we conducted the Mann-Whitney U test to see if the mutation-sensitivity and the order-specificity are significantly different between any two groups, because they are not normally distributed. The Mann-Whitney U test combines two groups and ranks them. Then, it calculates a statistic of the difference of the rank sum between two resampled groups. We used MedCalc  StatistiΩ, for tractable simulation. It consists of all ordered pairs of genes in the case of TGL network with a small number of nodes (|N| = 61), whereas 30,000 randomly selected gene pairs in the case of large-scale networks of HCS (|N| = 1192) and KEGG (|N| = 1659). Considering the different network size, we also set the time gap (T) to 2–20 in HCS and KEGG, and 1–10 in TGL, respectively.In this study, we simulated the ordered-mutation-inducing dynamics of three real biological networks using the Boolean network model (see Methods for details). As explained in Methods section, we note that a total of 1000 initial-states were randomly generated to compute the mutation-sensitivity and the order-specificity values in Eqs. (1) and (2) in all simulations. In addition, we constructed a set of ordered gene pairs to be investigated, δ) and order-specificity (Δ) values of examined gene pairs (Ω) in three signaling networks . In the figure, the y-axis value means the cumulative probability of mutation-sensitivity or order-specificity larger or equal to the x-axis value. We observed that the cumulative probabilities of δ ≥ 0.1 in HCS, KEGG, and TGL were 0.56, 0.62, and 0.39, respectively. This implies that it is not rare to observe that the network dynamics are sensitive against the double-mutations. It was also observed that the cumulative probabilities of Δ ≥ 0.1 in HCS, KEGG, and TGL were 0.38, 0.54, and 0.32, respectively. We need to note that an order-specificity of zero can be observed even in the case of gene pairs with nonzero mutation-sensitive values according to the definitions. Therefore, the observed distribution of the order-specificity implies that the mutation order is considerably critical to the network dynamics.To see how frequently the network dynamics are affected by ordered mutations, we examined the accumulative distributions of the mutation-sensitivity  in Ω into ‘Shorter-path direction’ and ‘Longer-path direction’ groups if l < l and l > l (see Methods for the definition), respectively, and forced knockout mutations in the order of vi and vj. We note that the gene pair  which is not bidirectionally connected was excluded from analysis to remove the effect of the connectedness factor on the dynamics. We compared the average mutation-sensitivity values between them . As shown in the figure, the mutation-sensitivity of the ‘Longer-path direction’ group is significantly higher than that of the ‘Shorter-path direction’ group in all signaling networks for most time gap parameter values. In other words, the network is more sensitive when the double knockout mutation occurs in the order inducing a longer path than in the reverse order. Next, we classified every ordered gene pair  into ‘More-paths direction’ and ‘Fewer-paths direction’ groups if n > n and n < n (see Methods for the definition), respectively, and forced knockout mutations in the order of vi and vj. We compared the average mutation-sensitivity values between them . As shown in the figure, the mutation-sensitivity of the former group is significantly smaller than that of the latter group in both signaling networks, almost irrespective of the time gap parameter. In other words, the network is more sensitive when the double knockout mutation occurs in the order involving fewer paths than in the reverse order. We note that our previous study showed that the dynamics influence from a gene on another gene is likely to be lessened as the path length increases and the number of paths decreases [P-values using the Mann-Whitney U test). As shown in the figure, the mutation-sensitivity of the former group is significantly smaller than that of the latter group in both signaling networks regardless of the time gap parameter. In addition, we further compared the order-specificity between the two groups . As shown in the figure, the values of ‘Non-DT → Non-DT’ and ‘DT → DT’ groups were highest and lowest, and they were the bounds for the values of other groups. Furthermore, the sensitivity of the ‘Non-DT → DT’ group was significantly higher than that of the ‘DT → Non-DT’ group, for most time gap values. Considering that these two groups are identical to each other except for the order in a gene pair, the result implies that the sensitivity difference was caused by only the mutation order. We further examined the order-specificity values of DT and Non-DT groups  and found that the former is larger than the latter. This finding is interesting considering that the mutation-sensitivity of ‘DT → DT’ was smaller than that of ‘Non-DT → Non-DT’ in Fig. roscovitine before doxorubicin is synthetically lethal in breast cancer cell [Some previous studies have investigated the characteristics of drug-target genes through network-based structural analysis , 55, andcer cell  and the cer cell . In addiΩ, ‘TSG → OCG’ and ‘OCG → TSG’. For every ordered pair of genes, we computed the mutation-sensitivity after forcing double knockout mutations according to the order of gene pair. Then, we compared the average mutation-sensitivity value between those two groups . As shown in the figure, the mutation-sensitivity value of the former group was significantly smaller than that of the latter group in all signaling networks, almost irrespective of the time gap. In other words, the network is more sensitive when oncogenes were mutated before tumor suppressors than the reverse order. In addition, we further compared the order-specificity between two groups, ‘TSG’ and ‘OCG’, and found that the order-specificity values of the former group were smaller than the latter group, almost irrespective of the time gap . This finding can be also related to some previous studies on the ordered mutations between oncogenes and tumor suppressor genes. For example, the double mutation in the order of TP53 and NOTCH, which are representative tumor-suppressor and oncogenes, respectively, was frequently observed in early stage of esophageal carcinoma patients [RAS, which is another oncogene, before loss of P53 formed a malignant tumor with metastatic behavior, but the reverse-ordered mutation resulted in benign tumors [It is known that tumor suppressors and oncogenes perform their cellular functions jointly in tumor progressions , 60, andpatients , 64. It n tumors , 65.FigIn this study, we defined the mutation-sensitivity and the order-specificity based on a Boolean network model to unravel the effects of ordered mutations on dynamics in signaling networks. It was interesting to observe that some structural properties of signaling networks can be a good indicator to explain the dynamical behavior with respect to ordered-mutation experiments. In addition, it was shown that various functionally important genes are related to the ordered-mutation-inducing dynamic. These results can enhance the understanding of the dynamic effects of ordered double-mutations on complex dynamics of large-scale biological systems, which supports the usefulness of our approach. Despite the usefulness of our approach, there are some limitations to be discussed. In this study, we employed the random nested canalyzing function to simulate the Boolean dynamics of the molecular signaling networks. This artificial specification can be a limitation of this study, although some previous studies have proven the usefulness of the model in fitting the update rules from the real biological data , 38. AnoMany previous studies investigated ordered mutations and found statistical relations with cancer development. Recently, these studies were extended to incorporate the analysis of biological networks. However, they are limited in identifying the significance of ordered mutations because they did not focus on analysis of the network dynamics. In this regard, we quantified the ordered-mutation-inducing dynamics by defining the mutation-sensitivity and the order-specificity measures using a Boolean network model. Specifically, they represent the probability that a network converges to a different attractor by a double knockout mutation, and the probability with which a network converges to different attractors by different mutation orders, respectively. It was not rare to observe both nonzero sensitivity and specificity values in large-scale signaling networks. In addition, we examined the relationship between the structural characteristics such as the path length, the number of paths, and the feedback loop with the ordered-mutation-inducing dynamics in the signaling networks. Interestingly, they showed significant relationships, which implies that such structural properties need to be considered in experimental studies with respect to ordered-mutation experiments. Next, we investigated the ordered-mutation-inducing dynamics of various functionally important genes. The numbers of drug-targets genes were negatively correlated to the mutation-sensitivity, whereas the network was more specific to the order of mutations subject to drug-targets genes than the rest genes. In addition, we found that tumor suppressors can efficiently suppress the amplification of oncogenes when the former genes are mutated earlier than the latter genes. Taken together, our results enhance the understanding of the dynamic effects of ordered double-mutations on complex dynamics of large-scale biological systems.Additional file 1 Figure S1. Relations of structural properties with ordered-mutation-inducing dynamics in BA network. A total of 250 BA random networks with |V| = 50 and |A| = 100 were generated. The time gap (T) was set to 1–10. (a) Mutation-sensitivity result with respect to the shortest path length. All pairs of nodes involving an FBL were classified into ‘Shorter-path direction’ and ‘Longer-path direction’ groups according that l < l and l > l, respectively. (b) Mutation-sensitivity result with respect to the number of paths. All pairs of nodes were classified into ‘More-paths direction’ and ‘Fewer-paths direction’ groups according that n > n and n < n, respectively. (c) Mutation-sensitivity result with respect to the FBLs. All pairs of nodes were classified into ‘FBL’ and ‘Non-FBL’ groups, according that any gene of the pair is involved by an FBL or not. (d) Order-specificity result with respect to the FBLs. All P-values were computed using the Mann-Whitney U test. Table S1. Gene information of HCS consisting 1192 genes, including its association with drug-target, tumor suppressor, and oncogene. Table S2. Gene information of KEGG consisting 1659 genes, including its association with drug-target, tumor suppressor, and oncogene. Table S3. Gene information of TGL consisting 61 genes, including its association with drug-target, tumor suppressor, and oncogene.


Correction to: Inj Epidemiol 7, 46 (2020)https://doi.org/10.1186/s40621-020-00272-zInserting the word ‘insidious’ in the first sentence to stet the author’s original text.Adding a ‘s’ to ‘invite’ in the last sentence so that the verb will match the singular subject of the sentence.In the original publication of this article Swanson, , the autThe publisher apologizes to the readers and authors for the inconvenience.The original publication has been corrected.


Glynne-Jones R, Sebag-Montefiore D, Meadows HM, et al. Best time to assess complete clinical response after chemoradiotherapy in squamous cell carcinoma of the anus (ACT II): a post-hoc analysis of randomised controlled phase 3 trial. Lancet Oncol 18: 347–562017; —This Article should have been published under the copyright “© The Authors. Published by Elsevier Ltd. This is an Open Access article under the CC BY license”. This correction has been made to the online version as of March 2, 2017.


In both, we suggest and solve various definitions of ge-synthesis, corresponding to different ways a designer may want to take hopefulness into account. We show that in all variants, ge-synthesis is not computationally harder than traditional synthesis, and can be implemented on top of existing tools. Our algorithms are based on careful combinations of nondeterministic and universal automata. We augment systems that ge-realize their specifications by monitors that provide satisfaction information. In the multi-valued setting, we provide both a worst-case analysis and an expectation-based one, the latter corresponding to an interaction with a stochastic environment.We study  Synthesis is the automated construction of a system from its specification: given a specification I and O of input and output signals, the goal is to construct a finite-state system that satisfies I, and responds with an assignment to the signals in O. Thus, with every input sequence, the system associates an output sequence. The system realizesocument}. At eachonments .autonomous systems, which interact with unexpected environments and often replace human behavior, which is only expected to be good enough. Throughout the paper, we construct products of automata whose state space is O. Accordingly, the product can be minimized to include only consistent pairs. Also, since traditional-synthesis algorithms, in particular the Safraless algorithms we use, can handle automata with generalized Büchi and co-Büchi acceptance condition, we need only one copy of the product.    [Determinancy of thege-synthesis game]. Determinancy of games implies that in traditional synthesis, a specification I/O-realizable iff O/I-realizable This is useful, for example when we want to synthesize a transducer of a bounded size and proceed simultaneously, aiming to synthesize either a system transducer that realizes ge-synthesis, simple dualization does not hold, but we do have determinancy in the sense that I/O-realizable iff O/I-realizable. Accordingly, ge-realizable iff the environment has a strategy that generates, for each output sequence ocument}. For ge-ge-synthesis is that we do not actually know whether the specification is satisfied. In this section we describe two ways to address this drawback. The first way goes beyond providing satisfaction information and enables the designer to partition the specification into to a strong component, which should be satisfied in all environments, and a weak component, which should be satisfied only in hopeful ones. The second way augments ge-realizing transducers by flags, raised to indicate the status of the satisfaction.A drawback of ge-realizability is suitable especially in settings where we design a system that has to do its best in all environments. ge-synthesis with a guarantee is suitable in settings where we want to make sure that some components of the specification are satisfied in all environment. Accordingly, a specification is an LTL formula ge-synthesizewith guaranteege-realizes x is hopeful for Recall that ge-synthesis with guarantee problem is 2EXPTIME-complete.The LTL ge-realizes ge-synthesis.    Consider an LTL formula mentclass2pt{minimL that have w as a prefix. We say that a word green forL if green forL if there is L. When a system is lucky to interact with an environment that generates a green input sequence, we want the system to react in a way that generates a green prefix, and then realizes the specification. Formally, we say that a strategy green realizesL if for every x is green for L, then L.light green forL if light green forL if there is L. It is not hard to see that for ge-realizable languages, green and light green coincide. Indeed, if L is universally satisfiable and ge-realizable, then L is realizable.For a language mentclass2pt{minimge-realizability is strictly stronger than green realizability.ge-realizes a specification fge-realizes f green realizes We first prove that every strategy ge-realizable. Let q before a value for Xp is known. Likewise, no word ge-synthesis coincide for ge-realizable.    We continue and describe a specification that is green realizable and not ge-realizing transducer has the desired property of being also green realizing. The second has to do with our goal of providing the user with information about the satisfaction status, in particular raising a green flag whenever a green prefix is detected. By Theorem ge-realizing transducer satisfies the specification. A naive way to detect green prefixes for a specification ge-realizing transducer, and raise the green flag whenever a green prefix is detected. This, however, requires a generation of ge-realizes the specification.Theorem L is universally satisfiable and ge-realizable, then L is realizable. Accordingly, given a transducer ge-realizes Recall that if Given an LTL formula M follows the subset construction of x iff x is not light green, and accepts it otherwise. Note that the definition of F involves universality checking, possibly via complementation, yet no determinization is required, and the size of Let Note that once we reach an accepting state in red forL if red forL if for all L. Thus, when the environment generates x, then no matter how the system responds, L is not satisfied.A word blue forL when blue forL if there is L. Thus, when the environment generates x, the system can respond in a way that guarantees satisfaction no matter how the interaction continues.a word Green flags provide information about satisfaction. Two additional flags of interest are related to safety and co-safety properties:L can be added to a transducer that ge-realizes L. As has been the case with the monitor for green prefixes, its construction is based on applying the subset construction on an NBW for L. It is tempting to interpret an expression like y such that y, we have that x is v-hopeful forge-synthesis:ge-synthesis with a threshold, the input is an v-hopeful has satisfaction value at least v. Formally, a function ge-realizes v if for every x is v-hopeful, then In ge-synthesis, the input is an ge-realizes x is v-hopeful, then In For a value x is hopeful, then ge-realization with a threshold is not monotone, in the sense that decreasing the threshold need not lead to ge-realization. Indeed, the lower is the threshold v, the more input sequences are v-helpful  difference function: The ratio function, given by some normalization to  of the function There are different ways to analyze the relation between The choice of an appropriate mentclass2pt{minimn-floor building. The environment sends to the controller requests, by means of a truth assignment to n, and is 1 when the slowest request is granted immediately. Sure enough, there is no controller that attains satisfaction value 1 on all input sequences, and so ge-realizability, we can synthesize a controller that behaves in an optimal way. For example, using the difference function, we measure the performance of the controller on an input sequence x. Note that such a best performance needs a look-ahead on requests yet to come, which is indeed the satisfaction value of x. Thus, the assumption off-line controller. Accordingly, using the ratio function, we can synthesize a system with the best competitive ratio for an on-line interaction. The two approaches taken in Sect. ge-synthesis with a threshold, we can use the function ge-synthesis (without a threshold), we can use the function ge-synthesis studied in Sects. ge-realizable, or is not. In particular, in case the specification is not ge-realizable, synthesis algorithms only return “no”. In this section we add a quantitative measure also to the underlying realizability question. We do so by assuming a stochastic environment, with a known distribution on the inputs sequences, and analyzing the expected performance of the system.The setting of probability distribution over I always holds in probability random variable is then a function X has a finite image V, which is the case in our setting, its expected value is X attains. Next, consider an eventconditional expectation ofX with respect toE is X(w) to X attains when restricting to words in E, and normalizing according to the probability of E itself.For completeness, we remind the reader of some basics of probability theory. For a comprehensive reference see e.g., . Let \doentclass1pt{minimahigh-quality synthesis problem Given an LTL formula a-la, indicating the announced satisfaction level. Thus, rather than talking about prefixes being green, red, or blue, we talk about them being v-green, v-red, and v-blue, for v is guarantees (in green and blue flags) or is impossible (in red ones). We can think of those as “degrees” of green, red, and blue. Below, we formalize this intuition and argue that even an augmentation of a transducer that ge-realizes quantitative language over L and a word v-green forL if v-realizable. That is, there is a transducer v-green forL if there is v-green for L. Thus, when the environment generates x, the system can respond in a way that would guarantee v-realizability. Finally, we say that L is green realizable if there is a strategy v and for every input v-green for L, we have that v-green for L. It is not hard to see that Theorem A ge-synthesis. Our complexity results are tight and show that ge-synthesis is not more complex than traditional synthesis. In practice, however, traditional synthesis algorithms do not scale well, and much research is devoted for the development of methods and heuristics for coping with the implementation challenges of synthesis. A natural future research direction is to extend these heuristics and methods for ge-synthesis. We mention here two specific examples.We introduced and solved several variants of GR(1) fragment [ge-synthesis, is not handled by its known algorithms, and is an interesting challenge. The success of SAT-based model-checking have led to the development of SAT-based synthesis algorithms[ge-synthesis. A related effort is bounded synthesis algorithms[Efficient synthesis algorithms have been developed for fragments of LTL. Most noragment , which sgorithms, where tgorithms, 24, whegorithms.


The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this paper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances. Nowadays, a China high-speed rail network has been formed, it is an urgent problem to design the Passenger Train Operation Plans (PTOP) based on networks, which is different from the general PTOP based on lines. Generally, there are two features in the PTOP that (1) passengers should be transported through the shortest path and (2) trains cannot visit any station more than once. So the PTOP based on networks can be refined as: There are several pickup-delivery demands (pd-pairs) and vehicles in a real-life connected graph. Each pd-pair chosen must be transported through the shortest path from the pickup point to the delivery point according to passenger/shipper requirements. Each vehicle starts at a given location and ends at the final delivery point of the pd-pairs transported by the vehicle, and cannot visit (stop at or pass through) any point more than once, namely each vehicle should travel along a real-life path. Constraints, such as vehicle load capacities, vehicle travel distances, and vehicle stops, need to be considered. This problem can be addressed by introducing a set of maximum-income routes to be driven by a fleet of vehicles to serve a group of known pd-pairs. Referred to as One-to-one Pickup and Delivery Problems with Shortest-path Transport along Real-life Paths (OPDPSTRP), this can be classed under One-to-one Pickup and Delivery Problem (OPDP). Since each pd-pair must be transported along the shortest path and vehicle stops need to be considered, the OPDPSTRP will be studied based on connected graphs, which shouldn’t be abstracted into complete graphs. The OPDPSTRP can also be applied in some transportation problems with these two features of the PTOP based on real-life connected graph, such as partial Taxi-sharing Problem. To the best of our knowledge, the OPDPSTRP has rarely been studied in the literature. So the model of the OPDPSTRP will be studied and efficient algorithms will be proposed for it in this paper.Section 2 presents related studies, while Section 3 studies the relationships between pd-pairs and presents the model for the OPDPSTRP. Section 4 presents a Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) based on 5 new neighborhoods for the OPDPSTRP. Section 5 proposes a set of random instances and analyses the efficiency of the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS for the OPDPSTRP. Finally, conclusions and future work are presented in Section 6.The OPDPSTRP belongs to the General Pickup and Delivery Problem (GPDP), which is an NP-hard problem.Many scholars have carried out research on the GPDP over the past few years, in response to numerous kinds of GPDP being applied in real-life, such as GPDP with Time Windows, Dynamic, Stochastic, Unpaired/Paired, Single/Multi vehicle, Single/Multi depot and Single/Multi commodity.Parragh et al. , 2] rev rev2] reThe GVRPPD can be further divided into two sub-classes: unpaired and paired. The first sub-class refers to situations where pickup and delivery locations are unpaired and each unit picked up can be used to fulfill the demands of any delivery customer, such as Many-to-many PDP . The seBerbeglia et al. , 10] di di10] diMost classical OPDPs are studied in complete graphs, and pickup points must be visited prior to delivery points  and ends at the final delivery point of the contents transported by the vehicle, so it can be considered as a multi-depot (vehicles) problem. Most OPDP research is based on single depot, such as that reviewed by Psaraftis , 13] , in which N = {1,…,n} for vertexes, E = {1,…,e} for edges, P = {1,…,p} for pd-pairs, and K = {1,…,m} for vehicles. Each pd-pair i with demand qi yields revenue πi. Each vehicle k∈K has a maximum capacity Qk and a fixed cost vck. The transportation cost per unit length of vehicle k is tck. Each vehicle k has a stop cost n.In order to define the proposed the OPDPSTRP in mathematical terms, we specify an connected graph The system also obeys the following assumptions.Each pd-pair attribute is different  is The total cost of each vehicle consists of constant cost, travel cost, and stop cost. In order to maximize income, not all pd-pairs need to be transported.There is only one shortest path between any two nodes in the graph.By defining the afore-mentioned problem, we hope to identify a suitable scheme to help optimize the benefit.The constants and variables used in this paper are listed in The model of the OPDPSTRP is formulated in this section, and the route structure of the OPDPSTRP will be studied for it in Section 3.4.i and j. Constraints (7) ensure that each pd-pair i is transported no more than once. Constraint (8) ensures that each vehicle is not over-loading. Constraint (9) determines whether the vehicle stops at node n or not. Constraint (10) ensures that the number of stops for each route (not including the depot/vehicle) does not exceed M. Constraint (11) determines whether edge e is traveled along or not. Constraints (12) ensure that each route with pd-pairs is assigned to one vehicle. Constraint (13) ensures that the length of each route (not including the depot/vehicle) is not longer than D. Constraints (14), (15), (16) and (17) introduce the decision variables.The objective function (1) maximizes the total profit, in which The route structure of the OPDPSTRP will be studied for the model.Definition 1: In a real-life connected graph, if all pd-pairs are transported through the shortest path in a route i starting with the first pickup point, and the route is a path, then it is defined that route i is Route-Structure-Feasible (RSF for short).Definition 2: If a RSF route stems from inserting pd-pair i into route j, then it is defined that pd-pair i can be inserted into route j according route structure. pd_R_rs_judgei,j is defined as the route structure feasibility judgement parameter of inserting  pd-pair i into route j.  is defined as the route structure feasibility judgement matrix of inserting (RSFJMI for short).Definition 3: If a RSF route is a combination of pd-pair i and pd-pair j, then it is defined that pd-pair i can be combined with pd-pair j according route structure. pd_combine_rs_judgei,j is defined as route structure feasibility judgement parameter of combining  pd-pair i with j.  is defined as the route structure feasibility judgement matrix of combining (RSFJMC for short). It is assumed that each pd-pair can combine with any vehicle, that is pd_combine_rs_judgep+1,j = 1.Definition 4: In a RSF route, if pd-pair j can be picked up not prior to vehicle/pd-pair i, then it is defined that pd-pair j can connect to vehicle/pd-pair i. The parameter connect_to_judgei,j  is defined as the judgment parameter for pd-pair j connecting to vehicle/pd-pair i. It is assumed that each pd-pair can connect to any vehicle, that is connect_to_judgep+1,j = 1. One vehicle cannot connect to another vehicle.Definition 5: If pd-pair i can connect to vehicle/pd-pair i , and pd-pair j can be delivered not prior to vehicle/pd-pair i, then it is defined that pd-pair j can connect after vehicle/pd-pair i. The parameter connect_after_judgei,j is defined as the judgment parameter for pd-pair j connecting after vehicle/pd-pair i. It is assumed that each pd-pair can connect after any vehicle, that is, connect_after_judgep+1,j =1.Definition 6: The nodes traveled by vehicle k in the route combined by pd-pair i and pd-pair j can be classified into stop nodes (stopped at by vehicle k) and pass nodes (passed but not stopped at by vehicle k). pi and di are pickup point and delivery point of pd-pair i correspondingly. sn_odi,n is defined as the judgment parameter of whether pd-pair i picks-up/delivers at node n.Definition 7: The sections in the route combined with pd-pair i and pd-pair j include weighting sections (sections traveled by a vehicle with pd-pairs), and connecting sections (sections traveled by a vehicle without pd-pairs). The constants lee and lci,j are defined as their lengths.i and pd-pair j in j connects to pd-pair i or not, and connect_after_judgei,j = 1 means pd-pair j can connect after pd-pair i, so j connects after pd-pair i successfully (Definition 4 and Definition 5). According to the above research, in a route combined with more than two pd-pairs/vehicle traveled by vehicle k, the lengths of the weighting sections and connecting sections can be formulated as k stopping at node n or not can be determined by Since Rule 1: Pd-pair j can connect to vehicle/pd-pair i when connect_to_judgei,j = 1.Rule 2: Each pd-pair transported by a vehicle must connect to the vehicle, or another pd-pair that connects after the third pd-pair or vehicle only once.Rule 3: Each vehicle/pd-pair must not be connected after by more than one pd-pair.Rule 4: Each pd-pair must not connect to itself.Rule 5: There cannot be circles in any route.Rule 6: Each pd-pair not being transported should not connect to any pd-pair or vehicle.Rule 1, Rule 4, Rule 5 and Rule 6 are apparent.i1, i2 and i3 are transported by vehicle k. The vehicle route must be as follows: pd-pair i1 connects after vehicle k (namely i2 connects to pd-pair i1 (namely i3 connects after pd-pair i1 (namely Rule 2 and Rule 3. If e5+e6+e7) between points di2 and di1 may be double-counted, because pd-pair i2 does not connect after any pd-pair or vehicle. If e1+e2+e3+e4+e5+e6+e7) between point k and di1 may be double-counted, as vehicle k has been connected after by pd-pair i1 already.Take All the rules have been considered in Section 3.3 .i5 can be inserted into route 1 while pd-pair i4 cannot; Pd-pair i3 can be combined with i1 while pd-pair i4 cannot; Pd-pair i2 and i3 can connect to pd-pair ii, pd-pair i4 can connect to pd-pair i5, and pd-pair i5 can connect to pd-pair i4; pd-pair i3 can connect after pd-pair i1 and i2, pd-pair i4 can connect after pd-pair i5, each pd-pairs can connect after all vehicles; Points 1 and 6 are vehicles locations, points 2, 3, 4, 15, 14, 12, 6, 8 and 10 are stop nodes; lck1,i1 = lee1, lci1,i3 = lee22.πi = 15, vck = 1, tck = 1, and Let So Cordeau et al.  presenteDefinition 3 in Section 3.4) were applied in neighborhood transform methods  to ensure that each selected pd-pair can be inserted into the selected route. The evolution of RSFJPC will be studied in Section 4.3.Additionally, studies of Grimault et al.  and Ho eInsert, pd-pair i  is selected randomly and inserted into a new route j chosen according pd_R_rs_judgei,j = 1.In i is inserted into route j2 from route j1, the scheme showed in r3 is removed from route j1 because there is no pd-pair requiring transportation from/to r3, while structure of route j2 remains the same. By reducing the number of stops, the route has been improved.As in Spread, a pd-pair is selected and inserted into a new route as an Insert operation. Should the vehicle be overloaded, the success rate can be improved by choosing a new pd-pair i from route and transferring this into a new route j selected by pd_R_rs_judgei,j = 1, and this cycle will continue until the vehicle is no longer overloaded, or if the cyclic number k exceed the preset iterative numbers controlling value K. The task of preset value K is to control the computing time of this operation.In i1 transported through route j1 is inserted into route j2, and the new scheme is shown in r4 is deleted from route j1 because there is no pd-pair requiring transportation from/to r4, and the structure of route j2 remains the same. Since the vehicle is overloaded at section r3-r4 in route j2, pd-pair i2 is selected from route j2 and inserted into j3, and then the new scheme is obtained as r3-r4, while the structure of route j3 remains unchanged, and the scheme is finally improved.As illustrated in Point-delete starts by choosing a route at random, before isolating the point with the minimal number picking stops and delivery stops on the route, and these pd-pairs i∈P are subsequently inserted into different routes j selected by pd_R_rs_judgei,j = 1, thus making it possible to delete the point from the first route.Point-delete is operated on stop point r4 in route j1, pd-pair i1 and i2 are inserted into route j2 and j3 respectively, and then the new scheme is obtained as r4 is deleted from route j1 because there is no pd-pair requiring transportation from/to it, while the structure of routes j2 and route j3 remains the same. The scheme is improved due to the reduction of stop point r4.As in Route-delete, net incomes nei of each route i are computed; route k is selected according to the probability Pk = nek/∑nei before being deleted from the scheme. All pd-pairs transported by route k are transferred to the state of non-carried. If there is no route with non positive net incomes, then the Point-delete should be executed.In the Reassign-vehicle is an Assignment Problem (AP) in which: rvi,j = 1 means route i being transported by vehicle j, and rv_benefiti,j is defined as its income. In this strategy, vehicles are reassigned to routes to achieve the best scheme by the Gurobi solver in Matlab.Reassign-vehicle may delivers the most significant change to the solution but cannot always improve the solution and requires more computer memory and time, it’s better to be chosen according to a low probability to perturb the local best solution, so a kind of Perturbation is proposed to shock the local best solution instead of Reassign-vehicle. In Perturbation, Insert, Spread, Point-delete, Rout-delete and Reassign-vehicle are chosen according to the operators choosing probabilitiesp1, p2, p3, p4 and p5 respectively.Since Insert, Spread, Point-delete, Rout-delete, and Perturbation are defined as operators opt(k) in this paper.Above all, Operators for routes construction and adjusting can be classed into three separate categories: pd-pair insertion, pd-pair deletion, and route deletion.Muelas et al.  arrayed ri and ri+1 in route R is the shortest path since all pd-pairs must be transported along the shortest path. Once pd-pair k needs to be inserted into route R(r1−r2−r3…rn), we have to find the right inserting location of pickup point pk and delivery point dk in route R first. Let ri and rj and let ri−rj−rk in route R. A point ri meeting the condition rj meeting the condition R. Finally, pk and dk need to be inserted into the rear of the two points respectively, and we may get three types of results as follows: both ri and rj can be found, only one of ri and rj can be found, neither ri nor rj can be found.Firstly, it is evident that the section between any two neighbor stop points ri and rj can be found:Both r−p−r−d−r➢ri and rj can be found, and i<j, the structure form of the new route R' must be r−p−r−d−r. In order to ensure feasibility of the route structure, pd-pair k should be transported along the shortest path in route R’, that is, k cannot be inserted into R. As in If both r−p−d−r➢ri and rj can be found, and i = j, the route structure form of R' must be r−p−d−r. In order to ensure feasibility of the route structure, ri−pk−dk must be the shortest path, that is, k cannot be inserted into route R. As in If both ➢ Other casesri and rj are found, and i>j, pd-pair k are opposite to route R and cannot be inserted into it, as in If both ri or rj satisfying the criteria, it must be sure that pk or dk is in route R already, then point pk or dk need not be inserted into it repeatedly. As in r2 is dk, so R(…r1−r2−r3…) remains the same after inserting dk into it.Because there is only one shortest path between any two nodes in this paper, if there is more than one ri and rj can be found:Only one of r−p−r−d➢ri can be found, the route structure form of R' must be r−p−r−d. Pd-pair k must be transported along the shortest path in route R', that is, k cannot be inserted into R. As in If only p−r−d−r➢rj can be found, the route structure form of R' must be p−r−d−r. Pd-pair k must be transported along the shortest path in route R', that is, k cannot be inserted into route R. As in If only ri nor rj can be found:Neither p−r−r−d➢ri and rj can be found, and R' must be p−r−r−d, pd-pair k is transported along the shortest path in route R', and the route structure must be feasible, that is, pd-pair k can be inserted into route R. As in If none of p−d−r−r➢ri nor rj are found, and k must be connected to the front of route R, the route structure form of R' must be p−d−r−r to minimize the length of R'. Set path(R) is the vehicle path which consists of all pass points in route R. Pd-pair k must be transported along the shortest path and each point must not be visited more than once in route R' to ensure feasibility of the route structure, that is, k cannot be inserted into route R. As in If neither r−r−p−d➢ri nor rj are found, and k must be connected to the back of route R, and the route structure form of route R' must be r−r−p−d to minimize the length of route R’. Pd-pair k must be transported along the shortest path and each point must not be visited more than once in route R' to ensure feasibility of the route structure, that is, If neither pk or dk needs to be deleted if there is no other pd-pair that needs picking up from it or delivering to it after deleting pd-pair k from route R. Otherwise, it should remain in route R.Point For Route-delete strategy, all pd-pairs are removed and route is deleted.pd_combine_rs_judgei,j] will remain the same, while RSFJMI  will change with the changes of route j. In order to update  quickly, some theories will be studied as follows.At each local search move step, RSFJMC ==0}, [pd_R_rs_judge] for route k’ can be updated by formula ==0}, and let L2 = {pl−dl}, a set of pd-pairs transported by route k'. [pd_R_rs_judge] for route k' can be updated by formula  is defined as the length between point k and point l.It is important to obtain a higher-level initial solution for such a large-scale and complex problem. In this paper, a generation method of initial solution is proposed, based on the idea of maximum saving. Algorithm 1 .Generation steps of initial solution are presented in Many Local Search (LS) meta-heuristics are studied for the VRP, such as the ALNS proposed by Ropke et al. , PisingeSince the major neighbourhood operator is pd-pair insertion and a choosing pd-pair need be inserted a fixed position in a route at each local search move step in the OPDPSTRP, solutions are not easy to be changed and always cannot be improved by only one operator obviously. That is to say that new methods which is different from traditional LS need be proposed for the OPDPSTRP. A basic VND and a basic VNS are proposed for the OPDPSTRP based on the above five neighborhoods. A new MS_VND and a new MS_VNS are developed to improve the efficiency of the proposing neighborhoods and algorithms in this paper.Algorithm 2  and Algorithm 3 .A VND and a VNS are processed to solve the OPDPSTRP, Pseudo-code of them are presented as in In order to achieve a near optimal solution of this problem, we propose a new MS_VND metaheuristic and a new Multi-Start Variable Neighborhood Search (MS_VNS) metaheuristic.Algorithm 4 .The steps of MS_VND in this paper are presented as in Algorithm 5 .The steps of MS_VNS in this paper are presented as in Algorithm 4 and Algorithm 5, the MS_VND and the MS_VNS have been improved in the following ways: (1) A Multi-start candidate solution set with size of n is acquired from the initial solution and updated to diversify the search, and parts of worse candidate solutions are replaced by the best solution according replacing proportion m if the solution is improving. (2) Five new operators  are utilized to improve the solution, which is different from traditional VNS. (3) In MS_VND, each candidate solution is transformed only once at a step (Multi-start-candidate-solution and One-operator), which is different from traditional LS . (4) A new local solution inferior to the primary one can also be accepted on the basis of two hypotheses: the iterations of that the solution keep the same are more than half of the presetting value, and the evaluation of the new solution is not drastically worse than the primary one.As in Insert<Spread<Point-delete<Route-delete<Perturbation according to the features of them. And this ranking will be tested further in Section 5.Changes and complexity ranking (from low to high) of operators can be primarily concluded as: To evaluate the performance of the VNS, the VND, the MS_VND and the MS_VNS, we designed 84 of the OPDPSTRP instances partitioned in small size connected graphs (3×4), medium size connected graphs (6×8) and large size connected graphs (10×10) at random. The Gurobi MIP solver (version 7.5.2) was used to compare with these approaches proposed in this paper. The following sections will describe the generation of instances, list the parameter values used in these approaches, and provide test results and optimality gaps.m0×m1−m2−m3−m4−L/H, in which m0×m1 is the size of a connected graph, each edge in this graph is deleted according to 1/m2, 1/m3 is the pd-pairs generation probability between each two nodes, 1/m4 is the vehicle generation percentage for each node and L/H is low or high cost. Consider instance 3×4-10-3-3-L as an example: the size of the incomplete digraph is 3×4(12 nodes and 144 node-pairs), the deletion probability of each edge is 1/10, pd-pair generation probability between each two nodes is 1/3, the vehicle generation percentage for each node is 1/3 and L means low cost. It has been checked that there is only one shortest path between any two nodes in each graph. Data of these 84 instances can be found in Each instance name has a format All experiments were conducted on a desktop equipped with an Intel(R) Core(TM) i7-4510U 2.00 gigahertz processor and 8 Gigabyte RAM. The operating system of this PC is a 64-bit Window 8. The Gurobi solver 7.5.2 was used to solve the MIP model, and all algorithms in this paper was coded in Matlab R2015a.The MIP model is solved by the Gurobi solver with termination conditions wherein computing time is over 108000 seconds or the Gurobi_Gap  is less than 5%. The long preset time aims to ensure that the Gurobi solver can obtain at least one feasible solution served as a comparison indicator with the proposed approaches, although in some cases it failed to achieve this goal. We have provided the upper bounds found by Gurobi solver as well, for a more in depth reference to the performance of the proposed approaches.The parameter setting of the algorithms have been tested based on 9 instances mention in Insert, Spread, Point-delete, Rout-delete and Perturbation  in these approaches, and the values of the parameters are gathered in According to The abbreviations of the experimental indicators and corresponding definitions are listed in Results solved by the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS are shown in Comparison of the average calculation efficiency of the VND, the VNS, the MS_VND and the MS_VNS are shown in Figs The above results shows that:CPU time of the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS are independent of road network scale. Numbers of pd-pairs and vehicles are the major influential factors to the CPU time of the Gurobi solver, numbers of pd-pairs are the major influential factors to the CPU time of the VND, the VNS, the MS_VND and the MS_VNS.Gap_Gurobi within an acceptable CPU time (108000 seconds) by Gurobi solver. Large instances with over 40000 (pd-pairs×vehicles) always cannot get feasible solutions within 108,000 seconds by the Gurobi solver.In general, instances with no more than 100 pd-pairs can get an optimum solution by the Gurobi solver in preset termination CPU time (108000 seconds). Instances with more than 5000 (pd-pairs×vehicles) always cannot receive the optimal solution with no more than 20% Gap to the Gurobi solver within an acceptable CPU time. The MS_VND can acquire the optimal solution with no more than 5% Gap to the Gurobi solver within an acceptable CPU time. The MS_VNS always takes a little more CPU time than the MS_VND to solve the instances with more pd-pairs.In almost all instances, the VND, the VNS, the MS_VND and the MS_VNS with the operators proposed in this paper always can acquire the optimal solution with no more than 10% The VND, the VNS, the MS_VND and the MS_VNS can even get better solutions than the Gurobi solver for the instances with large numbers of pd-pairs and vehicles.In almost all instances, the MS_VND significantly outperforms the VND, the VNS and the MS_VNS in terms of average solution quality Figs –24. The Gap to the Gurobi solver within an acceptable CPU time. In almost all instances, the MS_VND significantly outperforms the VND the VNS and the MS_VNS in terms of solution quality. The MS_VNS always takes a little more CPU time than the MS_VND to solve the instances with more pd-pairs. In the large instances, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.A new Pickup and Delivery Problem with new route structure, the OPDPSTRP, which is proposed in real-life connected graphs, is introduced and formulated in a new way. Five operators are proposed for the OPDPSTRP. A basic VND, a basic VND, a new MS_VND, and a new MS_VNS are developed for this problems and compared with the Gurobi solver. The test results show that the VND, the VNS, the MS_VND and the MS_VNS always can acquire the optimal solution with no more than 10% Our future work will concentrate on three aspects: (1) In order to improve the algorithm efficiency of the OPDPSTRP, path feasible strategy for neighborhoods will be studied. (2) There is only one shortest path between any two nodes in the connected graph in this paper, but there may be more than one shortest path between two nodes in some other real-life road networks, which we are going to study in the future. (3) The OPDPSTRP with time windows will be studied in the future.S1 Appendix(DOC)Click here for additional data file.S2 Appendix(DOC)Click here for additional data file.S3 Appendix(DOC)Click here for additional data file.S4 Appendix(DOC)Click here for additional data file.


Thanks to this representation, existing non-linear code typechecks as it is, and newly written linear code can be used with existing non-linear code in many cases. However, little is known about the type inference of OutsideIn(X) , we propose an inference system for a rank 1 qualified-typed variant of Bernardy et al. [2018] proposed a linear type system


Scientific Reports 10.1038/s41598-019-48216-y, published online 12 August 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word “underlying” was incorrectly given as “underling”. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file.


Action and vision are known to be tightly coupled with each other. In a previous study, we found that repeatedly grasping an object without any visual feedback might result in a perceptual aftereffect when the object was visually presented in the context of a perceptual judgement task. In this study, we explored whether and how such an effect could be modulated by presenting the object behind a transparent barrier. Our conjecture was that if perceptual judgment relies, in part at least, on the same processes and representations as those involved in action, then one should expect to find a slowdown in judgment performance when the target object looks to be out of reach. And this was what we actually found. This indicates that not only acting upon an object but also being prevented from acting upon it can affect how the object is perceptually judged. Action and vision are known to be tightly coupled with each other. Many studies show that visual perception might affect action. For instance, when visually presented with various objects, participants are faster in performing a compatible action, even when the action does not pertain to the viewed object , such as its shape (its being handled or not). We found that repeated grasping actions produced a perceptual after-effect, with participants being slower in detecting the visually presented handled mugs when their handles were oriented congruently with the grasping hand. Interestingly, the same effect did not occur when participants were asked to detect the visually presented mugs after repeatedly performing reach-to-touch actions  are processed motorically. In a behavioural study, we instructed participants to pantomime a reach-to-grasp action, with either the right or the left hand, on the presentation of a task-irrelevant go-signal. The go-signal was a 3D scene in which a mug, placed on a table, had the handle oriented toward the left or right, thus being congruent or incongruent with the pantomimed action. In half of the trials, the mug was located in front of a transparent plexiglas panel, whereas in the other half, it was located beyond the same panel, thus appearing to be out of reach. The results showed that participants were faster in responding with their reach-to-grasp pantomime when the handle of the mug was oriented congruently with the hand to be used, provided that the mug was presented in front of (but not behind) the plexiglas , respectively. Participants were all right-handed, with normal or corrected-to-normal vision, and with no history of either psychiatric or neurological disorders as self-reported. The study was approved by the local ethics committee and carried out in accordance with the principles of the revised Helsinki Declaration . Written informed consent was obtained from all the participants.Eighty participants were recruited and randomly assigned to each of four groups: Grasp-without-barrier (mean age ± s.d. = 22.40 ± 2.32), Touch-without-barrier (mean age ± s.d. = 22.35 ± 2.43), Grasp-with-barrier (mean age ± s.d. = 22.60 ± 3.57), and Touch-with-barrier  = 0.495, Experimental stimuli consisted of six pictures (1920 × 1040) representing a 3D room with a table and a mug on it, similar to the stimuli used in our previous study , so that each movement lasted approximately 1500 ms. Each participant performed 120 movements. A black box was used to prevent participants from seeing their own movement or the mug, and back tissue covered participants’ right hand throughout the motor training. Participants assigned to both the Touch-without-barrier and Touch-with-barrier groups were given different motor training: rather than reaching for and grasping the handle of the mug, participants assigned to these groups were asked to close their hands in a fist and repeatedly reach for and touch the mug with their knuckles.In the perceptual judgment task, participants sat in front of a 21-inch computer screen  at a viewing distance of 60 cm. They were asked to detect the presence or the absence of the handle by saying into a microphone “sì” (yes) when the handle was present and “no” otherwise. Each trial started with a fixation cross lasting 3000 ms, followed by one of the stimuli lasting 100 ms. After the stimulus, a response slide consisting of a black screen was displayed for 1900 ms  is different in terms of labial articulation and, consequently, in their acoustic wave forms. Since vocal reaction times are computed on the base of words’ wave forms, the criteria  by which we select vocal initiation of ‘yes’ and ‘no’ words are very different and, therefore, not directly comparable. Furthermore, in visual search tasks, reaction time (RT) is a roughly linear function of set size. Note that RTs will increase at a rate of approximately 20–30 ms/item for target-present trials and 40–60 ms/item for target-absent trials Wolfe , 2020. RIn line with previous studies on perceptual adaptation  with handle orientation (left vs. right) as a within-subject factor and group (1 vs. 2 vs. 3 vs. 4) as a between-subject factor. For all the statistical tests, the alpha level was set to 0.05. All multiple comparisons were Bonferroni corrected.p = 0.031, ηp2 = 0.066): participants were slower at detecting right-handled stimuli (Log-RT: 6.34 ± 0.01) than left-handled stimuli (Log-RT: 6.32 ± 0.01). Furthermore, ANOVA results revealed a main effect of group  = 3.384, p = 0.023, ηp2 = 0.13). Post hoc comparisons showed that RTs of participants assigned to the Grasp-with-barrier group (Log-RT: 6.4 ± 0.03) were slower than RTs of participants assigned to the Grasp-without-barrier group (Log-RT: 6.25 ± 0.01), no other comparisons were significant . Post hoc comparisons showed that RTs of participants assigned to the Grasp-without-barrier and Grasp-with-barrier groups were slower at detecting right-handled stimuli than left-handled stimuli . RTs of participants assigned to the Touch-without-barrier and Touch-with-barrier groups did not show any difference .Accuracy was equal or larger than 97% in all the groups and conditions, thus not further analyzed. ANOVA on RTs revealed a main effect of handle orientation  = 4.826, The aim of the present study was to investigate action–vision coupling by assessing whether and how making a visually presented object out of reach would impact on perceptual judgment. We, therefore, contrasted participants’ performance in judging the shape of a mug , which was sometimes presented behind a transparent barrier, immediately after motor training consisting of repeatedly executing either a reach-to-grasp or a reach-to-touch action without any visual feedback. There were two main findings.The first finding was that participants were slower in judging the shape of the visually presented mug when it was right-handled compared to when it was left-handled, with this effect occurring immediately after the reach-to-grasp motor training only. This finding replicates a previous study from our group  can be processed by a specific class of visuomotor neurons, that is, canonical neurons, which are typically recruited both when executing object-related actions, such as grasping, and when merely viewing objects with different sizes and shapes, without any intention to act on them (Jeannerod Even more interestingly, a recent study on canonical neurons in monkeys demonstrated that their responses dramatically decrease when the target object looked like as something that could not be acted upon, being either too far from the viewer or behind a barrier (Bonini, Maranesi, Livi, Fogassi, and Rizzolatti, Although further research is needed, our findings seem to enrich the view that visual perception can be affected by processes and representation involved in action preparation. Not only may acting on an object impact the way in which the object is perceptually judged, but also being prevented from acting on an object may also impact visual perception as measured by readiness to make perceptual judgements.