The invention of public-key cryptography (PKC) by Diffie and Hellman in 1976 is one of two milestones marking the beginning of modern cryptography. The security of a PKC system requires that it should be infeasible to compute the private key from a given public key, which in turn is typically guaranteed by the difficulty in solving some cryptographic-friendly mathematical problems. Among those problems, the integer factorization and discrete logarithm problems play pivotal roles in the development of public-key cryptography. In particular, the assumption that there is no polynomial time  algorithm that solves the above two problems constitutes the basis for the security of almost all currently used public-key cryptosystems, such as RSA and ElGamal. However, Shor [As a response to the quantum crisis, the research community has made many efforts to post-quantum cryptography (PQC) that are believed to resist quantum computer attacks. Lattice-based cryptography is one of the main directions in this area, and has become the most promising PQC candidate for standardization.The research of lattice-based cryptography dates back to the seminal work of Ajtai , which fFor current applications and standardization, key exchanges, public-key encryptions (PKEs) and signatures are the most desired lattice-based cryptosystems, where the first two are often used to ensure information secrecy, while the last provides information authentication. Note that public-key encryptions are equivalent to two-round key exchanges, also known as the key encapsulation mechanism (KEM). In the following, we focus on lattice-based PKEs/KEMs.f and its trapdoor f−1 are generated as the public key and private key. A plaintext m is encrypted as c = f(m), and the ciphertext is decrypted as m = f−1(c). The NTRU scheme and its variants follow such an approach. In the second approach, an approximate commutative function fs and a random input a are generated, the public key is ) and the private key is s. A plaintext m is encrypted as c1 = gr(a), c2 = gr(b) + E(m), where r is a random element, g is an approximate commutative one-way function and E is the encoding of an error-correction code. The ciphertext  is decrypted as m = D(c2 − fs(c1)), where D is the decoding of an error-correction code. The correctness of decryption is guaranteed by the approximate commutative property (gr(b) = gr(fs(a)) ≈ fs(gr(a)) = fs(c1)) and the error-correction code. Learning with errors (LWE) problem-based PKE/KEM schemes and their variants follow such an approach.The design principle of lattice-based PKEs/KEMs follows two approaches: a trapdoor one-way function and an approximate commutative one-way function. In the first approach, a trapdoor one-way function The standardization of PQC has received substantial support from national funding agencies, such as the European Union projects PQCrypto and SAFEcrypto. The USA National Institute of Standard and Technology (NIST) started the post-quantum standardization project in 2012, organized a worldwide ‘competition’ in 2016 and plans to deliver draft standards before 2024. After two rounds of evaluation, seven schemes were accepted as the round-three candidates on 22 July 2020, of which five are lattice-based schemes. In 2017, the International organization for standardization started a study project of post-quantum cryptography named SD8.Most LWE-based PKE schemes such as Kyber and LAC follow the Lindner-Peikert framework  up to thKyber  is one oLAC  uses sevet al. [By observing the asymmetries in lattice-based cryptosystems, Zhang and Yu et al.  proposedet al. [One important application of lattice-based PKEs/KEMs is to build authenticated key exchange (AKE), which could provide additional authentication to the established session key. There are several generic ways to construct AKE from lattice-based PKEs/KEMs. In the PKE setting, Xue and Lu et al.  proposedet al.  presenteet al. , which h


In CRYPTO 2019, Chen et al. showed how to construct pseudorandom functions (PRFs) from random permutations (RPs), and they gave one beyond-birthday secure construction from sum of Even-Mansour, namely  K is a uniformly random string with enough entropy, if for any input x, Random numbers are widely used in engineering practice. In particular, randomization is central to cryptography. One can generate random numbers by using physical random sources such as chaos-based  and quanIn theory, PRFs can be obtained from one-way functions ,6, but tAbout m independent n-to-n-bit keyed functions from m independent ideal random functions, its advantage does not depend on m. However, in this case the distinguisher still needs to make at least Fortunately, we can give positive answers to these questions. First, we prove that k randomly sampled from x.Second, we tweak the construction the work . A tweakFollowing the idea in , we solvx is an n-bit input, and n-bit uniformly random strings. Furthermore, we can tweak the construction t is a tweak, and x is an n-bit input.In this paper, we enhance the security of SoEM22  by showiP asx are the same as those in Equation (1). We tweak this new construction asx, and t are the same as those in Equation (2).Chen et al.  first cox (resp. the tweak t) in Equations (2) and (4) by an n-bit nonce N (resp. a message M), one can obtain two parallelizable beyond-birthday secure nonce based MACs asMoreover, from our two constructions of tweakble PRFs, we can give two nonce based MACs for variable length messages. In particular, when one replaces the input t is a tweak, and x is an n-bit input. Later, Dutta [P is a random permutation, and t, and x are the same as those in (7). Compared with Equations (7) and (8), our constructions in Equations (2) and (4) are parallelizable.Based on two random permutations i et al.  construcr, Dutta  gave a bP) asK is an n-bit key, x is an n-bit input, and 2 is a primitive element in the finite field K over n-bit uniformly random strings. However, all these two constructions were proved beyond-birthday secure only in the single-key setting. Compared with them, Equation (3) is parallelizable and can be proved beyond-birthday secure in the multi-key setting.Chakraborti et al.  construca et al.  proved tK is an n-bit key, N is an n-bit nonce, M is a variable length message, and Besides, Chakraborti et al.  also gavD who has access query to the primitive oracle P and to the construction oracle D is to distinguish which construction oracle it interacts with. Set p query-response tuples for the primitive oracle, and q query-response tuples for the construction oracle. Then, D interacts with The basic technique to prove the BBB security of our constructions is the H-Coefficient technique ,21. As aIn general, all possible transcripts are divided into bad transcripts and good transcripts. The key to use the H-Coefficient technique is to define bad transcripts in the ideal world with a low proportion. Furthermore, one also needs to show that the probability of any good transcript in the ideal world is close to its probability in the real world. After observing the transcript, the distinguisher will use this information to test whether it is compatible with P is large enough. Let P, and this idea allows that P, and P. Since For any good transcript, to prove that its probability in the real world is almost close to the one in the ideal world, it needs to show that the number of choices for unfixed maps of  idea in ,22 to coThe rest of this paper is organized as follows. In n-bit strings by s is sampled uniformly from S. For any sets q and N such that For any n-bit permutation-compatible set if n-bit permutation-compatible set n-bit permutation-compatible set For any function U and U is disjoint with x in Given two sets Definition 1Let n be a positive integer. Assume that . M be any binary string with M as s bits, and Next, we briefly describe an example of h family ,23 for sRemark 1.The keyed hash family One important tool used in our proofs is the H-Coefficient technique , which cr independent random permutations, and n-bit uniformly random strings. Then based on r public permutations Let m keyed functions m independent ideal random functions m independent keys. In this case, let As shown in Let (i)(ii)The security proofs in both multi-key and tweakable settings are similar. Therefore, we prove these two cases in a unified approach. For two independently and randomly sampled functions r independent random permutations. In this case, let D interacts with the construction oracle . LetN-size set S. When one samples S without replacement, N, Assume that there are The following lemma is useful in our proofs.Lemma 2.Let A, B, C, and N be positive integers satisfying Proof. In this section, we prove that the construction rm(n) in , namelyLet To show the security of Theorem 1.Let m independent random keys, and randomly samples two independent random functions In the multi-key setting, one sets Corollary 1.Let Corollary 1 shows that the construction Similarly, given an Corollary 2.Let Assume that Finally, let Corollary 3.Let Assume that for any message l is a constant, then If Proof of Theorem 1.For convenience, we follow some notations in ,17 in thWe denote(B-1): (B-2): (B-3): (B-4): (B-5): (B-6): (B-7): (B-8): (B-9): (B-10): (B-11): (B-12): (B-13): An attainable transcript Otherwise, we call The proportion of all bad transcripts in the ideal world is upper bounded by the following lemma.Lemma 3.Let Proof. y is sampled uniformly and independently from i) is denoted by Here we assume that there exists no repeated items in For each  that in ,17,22. HIn Lemma 4, we show that the probability of any good transcript Lemma 4.Let Proof. Given a good transcript The next goal is to lower bound Proposition 1.Let Proof. By definition, we have We use The way to compute those in  so that Finally, by Lemmas 1, 3, and 4, Theorem 1 can be proved.  □In this section, we first use one bidirectionally efficient random permutation Let As mentioned before, one can simultaneously show that the above two constructions are beyond-birthday secure in the multi-key and the tweakable settings by proving the BBB security of the “unified”function,Theorem 2.Assume that Same to Corollary 1, the following corollary holds.Corollary 4.Assume Similarly, given an Corollary 5.Assume Denote Corollary 6.Assume l is set to a constant, then Let Proof of Theorem 2.In this proof, we follow some notations in ,17 for cWe also denoteNow we define four parameters for transcript (C-1): (C-2): (C-3): (C-4): (C-5): (C-6): (C-7): (C-8): (C-9): (C-10):(C-11): (C-12): (C-13): (C-14): (C-15): (C-16): (C-17): For sets An attainable transcript Otherwise, i) for Let Lemma 5.Let Proof. p permutation pairs from the interaction between distinguisher D and P. For each distinct construction query y is sampled uniformly and independently from Let The probabilities of For For y for each Finally, by combining the upper bounds on In this part, we prove that for any good transcript Lemma 6.Assume that where Proof. Given a good transcript We first introduce some subsets of Proposition 2.Let Proof. By the definition of these five subsets, it holds that We use The next goal is to lower bound P is fixed on exactly p input-output pairs from U to V. For each For each P is fixed on exactly Now, we can define two disjoint collections P such that the event Let Let Recall that Similarly, it also holds that By the definition of Set Proposition 3.With notations as above, one has(i) All sets in (ii) Proof. We first prove (i). From the fact Next we prove (ii) by enumerating all possible cases. For For Now we define two disjoint union sets Let Conditioned on For each Definition 2.We say (1) (2) (3) (4) The next lemma shows that for each Lemma 7.Assume that where Proof. We count all possible pairs in a “good” set step by step as follows. First, we decide all possible pairs for After choosing After choosing S is unordered.When we finish the choice of all possible cases for Furthermore, P is well-defined by the definition of S:S, we define two subsets of P, P is fixed on For a fixed P is fixed on p input-output pairs from U to V, P.Until now, the random permutation Note that once the items in (i)(ii)Let k, and the second condition can exclude at most Now we count the number of all possible distinct tuples Let (i)(ii)Recall that k, and the second condition can exclude at most Now we count the number of all possible distinct tuples Let m be the number of all distinct tweaks appearing in m distinct tweaks. We denote m distinct tweaks asLet (i)For each (ii)For each For convenience, Except these two conditions, each Overall, by combining , 35), , , and 3737, one hombining  and 38)(38)p″(τ¯By combining  and 40)40), we cLower bounds on Putting , 43), a, a43), aPr[Tre=τ¯Combing all these facts together, the proof of Lemma 6 is finished.  □Finally, by Lemmas 1, 5 and 6, Theorem 2 follows.  □s Even-Mansours, namelys independent random permutations, and s n-bit uniformly random strings. Obliviously, this generalization is at least as secure as In this paper, we first prove the BBB security of the construction


Cell Death and Disease 10.1038/s41419-020-02835-w, published online 6 August 2020Correction to: The original version of this article unfortunately contained a mistake. After publication of the article, the authors noticed an unintentional error in Fig. 2f. As shown in Fig. 2f, the representative transmission electron microscopy image of “OL-shSec23a” was identical to the image of “POL-vector”. The authors have confirmed that the image of “OL-shSec23a” was mistakenly presented in the original Fig. 2f. This error was caused by unintentionally misplacing the representative image. Nevertheless, this error does not change the conclusion or the discussion of the article. The authors apologize for any inconvenience this error may cause. The corrected Fig. 2f is provided below. The original article has been corrected.


Whether intergroup conflict is a necessary condition for the evolution of human prosociality has been a matter of debate. At the center of the debate is the coevolutionary model of parochial altruism—that human cooperation with in-group members has coevolved with aggression toward out-group members. Studies using the intergroup prisoner’s dilemma–maximizing difference game to test the model have repeatedly shown that people do not exhibit out-group aggression, possibly because of an inappropriate operationalization and framing of out-group aggression. The coevolutionary model predicts out-group aggression when the actor understands that it will lead to the in-group’s benefit. However, in the game, such an aspect of out-group aggression that benefits the in-group is typically not well communicated to participants. Thus, this study tested the hypothesis that out-group aggression in the game would be promoted by a framing that emphasizes that attacking out-group members enhances the in-group’s gain. Results of two laboratory experiments with 176 Japanese university students in total showed that such a framing did not promote out-group aggression and individuals invested more money to cooperate with in-group members only, avoiding the strategy of cooperating with in-group members to harm out-group members. These results do not support the coevolutionary model. To understand the nature of intergroup conflict, researchers from diverse disciplines, such as sociology, political science, economics, and other social sciences, have conducted studies to unravel its causes6. In social psychology, intergroup conflict has been attributed to intergroup bias8, which is the human tendency to behave altruistically or cooperatively toward members of the group to which they belong  and/or competitively or aggressively toward members of the group to which they do not belong . Various theories have been proposed as a psychological explanation of it11.Intergroup conflict, including the extreme case of war, is ubiquitous in human social life14. However, based on an evolutionary perspective15, the absence of out-group aggression in previous studies may be due to the lack of a critical condition, such as a cue that attacking the out-group would increase the benefit to the in-group. Thus, the current study introduces such a cue to an experimental game paradigm and examines whether out-group aggression emerges.Recent experimental studies in social and evolutionary psychology have revealed that intergroup bias mainly stems from in-group cooperation, and out-group aggression rarely occurs in economic games16. Intergroup bias in minimal groups—in which no conflict of interest, negative stereotypes, or face-to-face interactions within or between groups exist—has been consistently observed in student17 and non-student samples18 across various cultures20. Evolutionary and social psychologists have formed several hypotheses on the evolutionary origin of intergroup bias22.Intergroup bias is present even between arbitrarily created experimental groups 24, which holds that humans simultaneously acquire in-group cooperation and out-group aggression. Choi and Bowles15 used an agent-based simulation and showed that agents who displayed both in-group and out-group aggression thrived, suggesting that in-group and out-group aggression co-evolved. The validity of the CO model has been examined using various datasets, ranging from ethnohistorical and archaeological25 to experimental27, although evidence for the model has been mixed30.One of the evolutionary hypotheses explaining intergroup bias is the coevolution model (CO model)22 is the assertion of the existence of out-group aggression. Previous studies have typically employed the intergroup prisoners’ dilemma–maximizing difference game (IPD–MD)12 to test the CO model experimentally. In the IPD–MD, players are randomly divided into two groups. They receive a fixed amount of money from the experimenter. They decide how much to keep for themselves and to invest in the two pools: the within-group and the between-group pools. The total amount of money invested in the within-group pool by the members of the group is doubled and divided among in-group members equally. However, the total amount of money invested in the between-group pool is doubled; all in-group members receive an equal split and out-group members lose half the amount of the money . Specifically, any investment in the between-group pool includes harming out-group members, i.e., out-group aggression. If people are inclined to pursue self-interest, they would keep the entire amount of the initial endowment for themselves. If people are inclined only to cooperate with in-group members, they will invest their money in the within-group and/or between-group pools, without distinguishing between the two pools. Meanwhile, if people intend to cooperate with in-group members and harm out-group members, they would invest in the between-group pool that reduces the resource of out-group members.A feature that distinguishes the CO model from other evolutionary models of intergroup bias31. Nevertheless, several studies have revealed that individuals, in general, invest more money in the within-group pool than in the between-group pool35. This pattern was also observed when researchers modified the game to encourage investment in the between-group pools41. Their findings offer conflicting evidence for the CO model: the empirical evidence does not suggest that individuals simultaneously acquire the tendency for in-group cooperation and out-group aggression.The CO model predicts that individuals are inclined to invest more in the between-group pool than in the within-group pool in the IPD–MDBehavioral evidence from studies using the IPD–MD does not support the CO model. Nonetheless, in-group and out-group aggression not evolving together would be a premature conclusion given the uncertainty of whether out-group aggression in the IPD–MD  corresponds to the operationalization of this concept in the CO model. Thus, the present study argues the vital importance of revisiting whether the IPD–MD offers contextual cues to elicit out-group aggression that is arguably acquired during evolution.43, and evolutionarily acquired psychological mechanisms are often characterized as domain-specific44. For instance, the percentage of accuracy in performing logical reasoning tasks increases when the task is framed to detect norm violators46. That is, “cheater detection” is thought to be an adaptive reasoning system specific to the domain of social exchange47. Previous studies have identified various domain-specific psychological systems47, including theory of mind48, intuitive physics49, and folk biology50. Moreover, intergroup bias is also considered a domain-specific feature51.Human minds are thought to have domain-general and domain-specific features52, and negative attitudes toward immigrants, who are associated with the possibility of unknown pathogens54. Cues of an important social exchange situation may also facilitate cooperation in a prisoner’s dilemma game56. If intergroup bias stems from an evolutionarily acquired domain-specific mindset51, then out-group aggression may be triggered by the cue of an adaptation task, such as intergroup conflict.Situational cues that imply a certain adaptive task reportedly activate a corresponding domain-specific mindset and behavior. For instance, disease priming, which induces pathogen infection threat assessment, leads to the preference for a symmetrical face, which indicates a high-functioning immune system15 described out-group aggressions predicted by the CO model as in-group-benefitting behavior. One of the main causes of intergroup conflicts is the competition for resources, such as food, territory, and mating opportunities59. The in-group-benefitting aspect of out-group aggression is an important tenet of out-group aggression in the CO model. Several evolutionary models and simulations suggest that out-group aggression might evolve when individuals gain resources from an out-group60. Moreover, people display hostile intergroup behavior when out-group resources can be acquired61; people also tend to be sensitive to threats arising from hostile intergroup relationships63. This suggests that out-group aggression is favored when it benefits the in-group.Choi and Bowles12. Thus, the in-group-benefitting aspect of out-group aggression seems to be missing in the IPD–MD, and this might be why previous studies using the game have yielded inconsistent results with the CO model.However, out-group aggression in IPD–MD seems to show a discrepancy with how it has been theoretically defined in the CO model. Specifically, previous studies using the IPD–MD have operationalized out-group aggression as simply reducing the payoff of out-group members: investment in the between-group pool is typically framed as merely about increasing and decreasing payoffs for in-group and out-group members, respectivelyThe present research aimed to test the framing effect in an IPD–MD. Specifically, if out-group aggression in an IPD–MD  is framed such that it leads to financial gain for the in-group, then out-group aggression would emerge, which provides empirical support for the CO model.64, for example, the gain or loss framing on risky decision making65, attribute framing on evaluation64 and goal framing on cooperation66. Furthermore, the framing effect has been observed for evolutionary acquired domain-specific psychology67. This study examines whether out-group aggression would emerge when the contribution to the between-group pool is framed as having benefits to the in-group. Specifically, this study formulated two conditions that varied in the framing of the between-group pool: a control condition and a steal framing condition. In the former, the instructions on the two pools were identical to that of a basic IPD–MD. In the latter condition, the investment in the between-group pool was framed such that it led to moving money  from an out-group to their own group.Previous studies have revealed the framing effect on human decision making31 proposed the “weak” and “strong” hypotheses of out-group aggression based on the CO model: the amount invested in the between-group pool should be interpreted not only in terms of its absolute amount but also as a relative amount compared with the amount invested in the within-group pool, and “a larger contribution to the between-group pool relative to the within-group pool may be interpreted as negative attitude toward the out-group, an equal contribution to both pools as indifference regarding the out-group’s welfare, and a smaller contribution to the between-group pool as positive attitude toward the out-group”13 (p. 2). Based on the CO model, a negative attitude toward the out-group can be expected to lead to aggressive behavior in the steal-framing condition. Therefore, the present study set the “strong” hypothesis (hypothesis S) as follows:The current research tested two hypotheses regarding the framing effect on out-group aggression. BöhmIn the steal condition, individuals would contribute more to the between-group pool than to the within-group pool.68, steal framing may nonetheless lead to a less positive attitude. Therefore, the current study set the “weak” hypothesis (hypothesis W) as follows:Even if hypothesis S is not supported, as in previous studiesIndividuals in the steal condition would invest more money in the between-group pool than those in the control condition.69. Preference tends to be stable regardless of the actions and reactions of an interacting partner. Meanwhile, belief refers to an expectation about others’ behavior. If the framing affected the investment in an IPD–MD, then whether the effect would be attributable to changes in preferences and/or beliefs merits investigation.The research aimed to further explore how the steal framing would influence out-group aggression. Framing effects in experimental economic games can be divided into effects of changes in preference and beliefStudy 1 was reviewed and approved by the ethical committee at Kochi University of Technology. In accordance with the Declaration of Helsinki, all participants provided written informed consent.The study was advertised in a large student-participant pool at Kochi University of Technology, and 73 participants (34 women) voluntarily participated in the current study. Their mean age was 19.53 years (SD = 1.12).Upon arrival at the experimental lab, participants were given a participant ID and instructed not to share it with anyone. They were then escorted individually to an experimental cubicle, in which they completed the study on a computer without the physical presence of others. Once they were seated, they received instructions about the IPD–MD. Participants were first randomly divided into two groups, and each was given 600 JPY by the experimenter. Next, they had a one-shot interaction in which they each decided how much of the 600 JPY to keep for themselves and to invest in the within- and inter-group pools. The amount invested in the within-group pool was doubled by the experimenter and the total was distributed equally to all members of the participants’ own group.Participants were randomly assigned to one of the two framing conditions  and received different instructions on the between-group pool. In the control condition, they were informed that the total amount invested in the pool would be doubled and then distributed equally among in-group members regardless of their contribution. Moreover, they were told that out-group members would lose half the amount of money that in-group members received. The only difference between the control and the steal framing condition was whether the money invested in the between-group pool increased the in-group resource or decreased the out-group resource, as per the experimenter. For the control condition, the instructions mentioned that the experimenter increased the in-group’s money and decreased the out-group’s money. Specifically, in a game between Groups X and Y, each of which has five participants, if Participant A from Group X invests 100 JPY in the between-group pool, the experimenter doubles the amount of money and distributes it equally among the five participants. Therefore, all participants in Group X, including participant A, would receive 40 JPY each. Simultaneously, the experimenter deducts 20 JPY from each of the five participants in Group Y. Meanwhile, in the steal condition, the amount of money invested in the between-group pool moves from the out-group to the in-group. For example, if Participant A of Group X invests 100 JPY in the between-group pool, all members of Group X, including A, would receive 20 JPY each. They receive an additional 20 JPY that is taken from out-group members. In other words, the amount of money deducted from Group Y is given to Group X. Thus, the payoff structure of each individual was identical in both conditions. The word “steal” was not used in the instructions including the steal framing condition. The participants were told that all of them would decide simultaneously and that they could complete the game only once. It was also emphasized that the rules of the game were the same for out-group members. After reading the instructions about the IPD–MD, the participants input their decisions on a computer screen.The participants then completed a post-experiment questionnaire. They first answered the comprehension and manipulation check questions. The tool contained three comprehension check questions: (C1) “Whose money does the investment in the within-group pool increase?” (C2) “Whose money does the investment in the between-group pool increase?” and (C3) “Whose money does the investment in the between-group pool increase?” They selected one of the following options: “increase (decrease) the money of my group as a whole,” “increase (decrease) the money of others’ group as a whole,” “increase (decrease) the money of both groups,” “increase (decrease) the money of neither group,” or “don’t know.” For the manipulation check, they were asked the following question: “Who received the money subtracted from the members of the other group owing to the investment in the between-group pool?” They answered this with one of the following options: “the money went to my group,” “the experimenter collected the money,” or “I don’t know.”After the comprehension and manipulation checks, the participants inferred how other members of their own group and the other group had completed the game. Specifically, they were asked how much other members of their ingroup and outgroup had kept and invested in the within- and between-group pools, in units of 50 JPY. For exploratory analyses, the study administered items measuring identification with the in-group and out-group and social dominance orientation (see ps > 0.05). The participants’ understanding of the rules of the game was satisfactory. The correct response rate for the manipulation check was 94.5%. In the control condition, 89.2% of the participants answered correctly, and 10.8% answered incorrectly or chose “I don’t know.” All participants in the steal condition answered correctly. The correct response rate between the two conditions showed no significant difference . As most of the participants correctly answered the comprehension and manipulation check questions, we did not conduct data exclusion. Data exclusion based on these questions did not change results in a meaningful manner  × 2 (pool: within- vs. between-group) mixed ANOVA. The results showed a significant main effect of pool, F = 14.33, p < 0.001, ηp2 = 0.17. The main effects of framing  = 0.54, p = 0.465, ηp2 = 0.01) and the interaction effect  = 0.004, p = 0.953, ηp2 < 0.001) were insignificant.On average, participants kept 397.26 JPY SD = 191.10), invested 147.95 JPY (SD = 171.28) in the within-group pool, and invested 54.79 JPY (SD = 103.47) in the between-group pool. The means and standard deviations of their investments under different conditions are shown in Fig. 91.10, int(71) = 0.74, p = 0.46, d = 0.17). In the steal condition, the participants invested a significantly lower amount in the between-group pool than the within-group pool  = 2.75, p = 0.009, d = 0.68). Therefore, hypotheses S and W were not supported. Using G*Power 3.169, sensitivity analysis of a two tailed t-test (power = 0.8) for hypothesis S revealed that the detectable effect size was 0.665 and that for hypothesis W was 0.48. This suggests that the observed effect sizes, especially for hypothesis S, were not big enough for the current study to detect.The mean amount of investment in the between-group pool was 45.94 JPY (SD = 100.95) in the control condition and 63.89 JPY (SD = 106.64) in the steal condition, with no significant difference between them  = 29.26, p < 0.001, ηp2 = . 29. The main effect of framing  = 1.90, p = 0.173, ηp2 = 0.03) and the interaction effect  = 0.16, p = 0.690, ηp2 = 0.002) were not significant. Thus, the steal framing did not alter the expectation about how other in-group members would complete the game.Although the effect of the framing manipulation was not significant, we examined the participants’ inferences about other in-group and out-group members’ investment decisions  = 23.15, p < 0.001, ηp2 = 0.25. The main effect of framing  = 1.09, p = 0.299, ηp2 = 0.02) and the interaction effect  = 1.55, p = 0.217, ηp2 = 0.02) were not significant. This indicates that the framing did not alter the behavioral expectation of out-group members.Further, the A 2 (framing) × 2 (pool) mixed ANOVA on the estimated amount of money invested by out-group members revealed a significant main effect of pool, Both hypotheses were not supported in Study 1: results showed that steal framing did not increase out-group aggression in IPD–MD. Thus, even when out-group aggression was framed as being beneficial for the in-group, the CO model was not empirically supported.68; except for Halevy et al.40. As per the sensitivity analysis, the hypotheses were not supported, possibly due to the small sample size. Thus, we conducted Study 2 with more participants and re-tested the hypotheses.Study 1 had fewer than 40 participants in each condition, smaller than the number of participants recruited in the majority of studies that used the IPD–MDStudy 2 was reviewed and approved by the ethical committee at the Kochi University of Technology. In accordance with the Declaration of Helsinki, all participants provided written informed consent.Study 2 intended to recruit 50 participants for each condition. A total of 107 Japanese undergraduate students signed up for the study . Their mean age was 18.87 years (SD = 1.18). Participants were recruited from a large participant pool at Kochi University of Technology with an emphasis on monetary incentives. The procedure and materials were identical to those in study 1.ps > 0.05). The correct response rate for the manipulation check item was 91.3%. In the control condition, 83.3% of the participants answered it correctly, and 16.7% answered it incorrectly or chose “I don’t know.” All (100%) the participants answered correctly in the steal condition, and the difference was significant (Fisher’s exact test: p = 0.003). The exclusion of participants in the control condition who failed to answer the questions correctly did not change the results of subsequent analyses in a meaningful way. Thus, results without data exclusion are reported here  = 7.72, p = 0.007, ηp2 = 0.07) and a significant interaction effect  = 4.06, p = 0.047, ηp2 = 0.04). In contrast, the main effect of framing was not significant, F = 2.06, p = 0.154, ηp2 = 0.02. Post hoc comparisons using the Holm method revealed that the amount of investment in the within-group pool was higher in the steal condition than that in the control condition (p = 0.014), but the difference in investment in the between-group pool between the two conditions was not significant (p = 0.518). In addition, the amount of investment between the within- and between-group pools in the control condition did not significantly differ (p = 0.581). Meanwhile, the difference in the steal condition was significant (p = 0.001).The participants, on average, kept 352.43 JPY (SD = 202.84) for themselves and contributed 156.31 JPY (SD = 170.31) and 91.26 JPY (SD = 150.72) to the within- and between-group pools, respectively  = 0.68, p = 0.497, d = 0.13). In the steal condition, the amount invested in the between-group pool was significantly lower than that in the within-group pool  = 3.18, p = 0.003, d = 0.70). Therefore, hypotheses S and W were not supported. Sensitivity analysis of a two tailed t-test (power = 0.8) for hypothesis S revealed that the detectable effect size was 0.558 and that for hypothesis W was 0.408. This suggests that the observed effect sizes, especially for hypothesis S, were not big enough for the current study to detect.The mean amount of investment in the between-group pool was 100.93 JPY (SD = 156.76) in the control condition and 80.61 JPY (SD = 144.63) in the steal condition, with no significant difference between them  = 15.32, p < 0.001, ηp2 = 0.13) and the interaction effect  = 5.36, p = 0.023, ηp2 = 0.05) were significant. Meanwhile, the main effect of framing was not significant, F = 2.8, p = 0.097, ηp2 = 0.03. Post hoc pairwise comparisons with the Holm method revealed that the level of inferred investment in the between-group pool was not different between the two framing conditions (p = 0.52). In contrast, the inferred investment in the within-group pool in the steal condition was significantly higher compared with that of the control condition (p = 0.005). These results showed that although steal framing increased the inference of cooperation among in-group members, it did not increase the inference that other in-group members would attack out-group members.We examined the participants’ inferences about other in-group and out-group members’ investment decisions  = 7.19, p = 0.009, ηp2 = 0.07) and pool  = 15.35, p < 0.001, ηp2 = 0.13) were significant. The interaction effect was not significant  = 3.7, p = 0.057, ηp2 = 0.04). Thus, steal framing generated an inference that out-group members would no longer pursue self-interest, but this did not mean that they would invest more in out-group aggression.The same ANOVA on the inferred investment out-group members revealed that the main effect of framing  does not promote out-group aggression.Previous studies using experimental economic games, such as the public goods game, have shown that framing can change behavior68. These findings support another evolutionary model of intergroup bias, namely, bounded generalized reciprocity (BGR)74. The BGR model holds that in-group bias stems from cooperation with in-group members rather than aggression toward out-group members75. The BGR model assumes that people have an intuitive belief that indirect reciprocity exists within the group, and that acting cooperatively toward in-group members is of vital importance to establishing a good reputation. However, individuals do not suppose that out-group members are part of the system of indirect reciprocity, and consequently, they are not motivated to display altruistic behavior to earn a reputation not only with respect to out-group members but also strangers. In other words, the BGR model assumes that humans do not act altruistically toward out-group members, not that they proactively attack them. Although the current study did not aim to validate the BGR model, the results are consistent with the model.In the current study, regardless of the framing condition, the amount of investment in the between-group pool was not higher than that in the within-group pool, consistent with previous findings77. For example, Böhm et al.36 showed that, although not the framing manipulation, the amount of investment in the between-group pool increases when it can prevent attacks from the out-group. Additionally, the framing instruction used in Weisel and Zultan68, which supports the “weak hypothesis” in IPD–MD, seems to have an in-group defense-like phrase. Further research could investigate whether out-group aggression can occur by setting framing characterized by a defensive function.Out-group aggression can emerge when it can defend an ingroup78 but also for the conflicting empirical findings80. These do not necessarily mean, however, that humans have not evolutionarily acquired any aggressive tendency toward out-group members. There may be several types of out-group aggression76 that are possibly suited for the CO model, for example, preemptive strikes81 and proactive or reactive aggression82. A theoretical and empirical examination of the types of aggression directed toward out-group members is necessary.The CO model has been criticized not only for its theoretical assumptions84, the effect size of d = 0.17 obtained in study 1 was relatively small. Additionally, the effect size of d = 0.13 obtained in study 2 was in the opposite direction of study 1, and the combined effect size of study 1 and 2 was close to zero (d = 0.04, see There are other two limitations. First, framing manipulation was used to emphasize that out-group aggression increases the benefit of the in-group, but it is not clear whether the framing changed the participants’ perception as intended. That said, participants in the steal framing condition might see the investment in the between-group pool as a means to decrease the benefit of the out-group rather than increase the benefit of the in-group. In that case, they might refrain from investing money in the between-group pool because it would be socially undesirable. Second, as per the sensitivity analysis, the effect may not have been detected because the sample size was small. Compared to the effect sizes obtained in previous meta-analyses on the gain–loss framingSupplementary Information.


In intensive transactional analysis psychotherapy (ITAP), intensity is obtained with both technical expedients and the relational manner with the patient. In ITAP, the therapist modulates pressure and support commensurately to the patients' ego strength. In the present article, we contrast two clinical cases of young adults in which ego strength produced different therapy outcomes and processes. We present excerpts of the psychotherapy process that illustrates technical aspects of ITAP as well as the therapist's attitude that we describe as holding. We show quantitative therapy outcomes consisting of effects size values of changes in Clinical Outcome in Routine Evaluation—Outcome Measure scores in baseline, treatment, and follow-up phases and qualitative outcome evaluated with the Change Interview at the end of the therapy. In the patient with high ego strength, we observed a rapid improvement and a complete recovery at the end of the therapy, whereas the results of the patient with low ego strength were less consistent . We conclude that quantitative and qualitative outcome data, together with process observations, are required to have a complete picture of therapy effectiveness. Moreover, we conclude that qualitative ego strength is not a limitation for the use of expressive therapy such as ITAP, but rather, it is an important variable that should be considered to dose confrontations and support. Intending to increase intensity in therapeutic intervention, intensive transactional analysis psychotherapy (ITAP) is short-term psychodynamic psychotherapy that integrates transactional analysis Berne,  with briimpulse is a manifestation of the Id  are explored, comparing them with relational experiences with the therapist in psychotherapy sessions (therapeutic relationship) and with past relationships in which repetitive relational patterns may have been formed as an effect of traumatic experiences. Thus, in the ITAP model, psychic functioning is described as interconnections of impulse, anxiety, and defenses, which have originated in past relationships and which can be enacted in here-and-now relationships (current relationships and/or therapeutic relationship) . CORE-OM global scores allowed the classification of the patients on the basis of their distress level: healthy (score <0.6), low-level (score between 0.6 and 1.0), mild (score between 1.0 and 1.5), moderate (score between 1.5 and 2.0), moderately severe (score between 2.0 and 2.5), or severe (score >2.5). Moreover, four subscales allowed the evaluation of four outcome variables: well-being, psychological problems , functioning , and risk (risk to self and others). The Italian version of the CORE-OM shows good acceptability, internal consistency, and convergent validity . The CORE-OM is a widely used scale for the routine evaluation of psychotherapy outcomes ; (b) how likely these changes would have been without therapy (from 1 = unlikely to 5 = likely without therapy), and (c) how important he/she feels these changes to be (from 1 = slightly important to 5 = extremely important).Psychotherapy outcome was evaluated qualitatively through The Change Interview, a semi-structured interview that provides qualitative descriptions from patients of perceived change reported at the end of the therapy  diagnosis was provided for each patient, and they were asked about the goals of their therapy before starting the treatment. For both patients, this was the first experience of psychotherapy, and they were not treated pharmacologically.well-integrated structure according to the OPD-2 diagnosis. She was a 25-year-old female student. In her therapy, she focused mainly on her relational difficulties. She reported having difficulties in regulating her emotions with others. On the one hand, she suffered because sometimes she was aggressive with others, and then, she felt guilty as a consequence of this aggressiveness. On the other hand, she perceived not being free to express herself with her family, and she wanted to feel free to make her own decisions. She also suffered from anxiety and loss of concentration. In addition to these emotional difficulties, she wanted to cope with the loss of her dog (which was living with her ex-partner). With regard to the diagnosis, she saturated the DSM-5 criteria for dysthymic disorder and generalized anxiety disorder  and clinical training as psychotherapists and three advanced students. Two of the experienced researchers also had specific training as psychotherapy supervisors. The students participated in research team/clinical supervision groups, and they were also involved in data collection and analyses.Patients were recruited from a waiting list of students who had psychological or relational difficulties and were voluntarily referred to therapy as part of a larger clinical study. The patients were voluntary students attending the same university as the research team, but they had no direct connection with the research team. The Ethical Committee of the University of Padua approved the research protocol. Before entering treatment, all patients received detailed descriptions of the research protocol, and they were informed that they were free to leave the research protocol at any moment without consequences for the continuation of their therapy. In the informed consent, a specific section for the use of video-recorded sessions was included, and it was specified that patients would not be identifiable on the basis of the material presented in scientific publications.Baseline included 5 weekly evaluations in 5 consecutive weeks before the beginning of the therapy ; (b) treatment included weekly evaluations realized immediately before each session ; (c) follow-up included evaluations realized at 1, 3, and 6 months after the end of the therapy. For each assessment, patients filled out the CORE-OM in the clinical psychology laboratory and in the presence of an external research assistant. During the first follow-up, a researcher carried out the Change Interview to collect qualitative data concerning patients' subjective perception of changes. Patients were informed that the therapist had no access to any research data provided.For the evaluation of psychotherapy outcome time series, longitudinal data were collected in three different phases: (a) The treatment followed the procedures described in the ITAP manual  were dropped unless they had specific communication value. In brackets, we reported the position in the intrapsychic triangle  and interpersonal triangle . Regarding the therapist's interventions, the positions to which the therapist moves are preceded by the symbol → . In few cases, interventions escape from triangle classifications. Thus, we provided few additional categories. “Aw” refers to therapists' interventions aimed at stimulating aspects of awareness in the patients (→Aw) and the patient's responses indicating the acquisition of aspects of awareness (Aw); “E” refers to empathic interventions; “Al” refers to therapists' interventions aimed at the alliance. According to the consensual qualitative research method : she recently encountered a dog similar to the one she had to leave with her ex-boyfriend and became sad. The therapist aims to bring out the impulses activated in this episode by comparing the patient's defensive modes (D) in the here-and-now of therapy (T) to the emotions related to the loss of the dog (I). The patient is able to achieve a greater awareness regarding her tendency not to face conflict situations by giving in to the will of others (such as leaving her beloved dog to her ex-boyfriend).What did you feel in that moment? [→ I/C]T: I don't know how to express it, I mean it was really a strange thing…a lump in my throat… [A/C]M: How was this lump in the throat for you? [→ A/C]T: Nice and bad…Nice because it was nice, I mean, ah, it took my back to another world in a moment … And bad because once it's finished you think in any case “Who knows what will happen to my dog…” [D/C]M: As if you'd realized that that scene isn't there anymore?… How did you feel in that moment? [→ I/C]T: Ah, the darkness takes you [I/C]M: You mean, this scene was sad? [→ I/C]T: Yes, yes, also. Even now that I'm talking about I feel the darkness returning, yes … [I/T]M: Yes, but you're laughing a lot [→ D/T]T: Ah I know, well, unfortunately it's a bad habit of mine, laughing [D/T]M: No, I have the impression that there's a part of you that's sad, and another part that says “No, no, come on, everything is ok, laugh about it” [→ D/T]. But a part of you is sad [→ I/T]T: Ah yes, I can't get rid of it, I mean I can't get rid of a piece of my life, get rid of some memories. No? [Aw/C]M: But the memories are sad… [→ I/T]T: Ah yes, but, but you've got to deal with them [D/T]M: And how do you deal with them? IF you deal with them by laughing and then they come back [→ D/T].T: Ah… I don't know another way… I mean the time, I've always said “In time things will pass”, sure enough time has passed a lot, ah, I mean that … [D/T]M: Yes of course. I was concerned about the part, actually, that is worried …that then becomes darkness … [→ A/T]T: I hope not. I mean, I hope that… this doesn't happen, I hope so. I mean every day of my life … to do things that make me so satisfied that I don't think of anything else, no? [D/T]M: I have the impression that not thinking about it creates a, sort of, barrier for a bit [→ D], then something bigger comes along … [→ I/T]T:…Yes, yes, I've thought about this … [Aw/T]M: the barrier collapses and everything that wasn't there before comes along … [→ D/T]T: …Yes, yes, it's true … [Aw/T]M: And I'm worried about this, because the barrier of doing stuff so as not to feel what there is over here [mimes a barrier with the hand], it holds up a little, a little and then by dint of doing this you get all of the manifestations , and then, as is natural, it collapses. And when it collapses it's a month and a half, two, of darkness. [→ D/T]T: …What are you in contact with? [→ I/T]T: I don't know what, I don't know what this thing inside of me is, I'm trying to bring out something that's inside me that I don't know. [D/T]M: On a cognitive level yes, I have the impression that you don't know. On an emotional level how are you, when you think of these things? Actually, when do you feel this thing?…Let's try to remain there, to listen to what's there, behind that barrier that I was talking about before …[→ I/T]T: I don't know, because I was different, I was like other people, as if I was talking about other people, a lot of things have changed, so I can no longer reflect myself in what I was. I have really changed personality so I can't remember anything at all. [D/T]M: [Silence] What is it that's coming back then…? [→ I/T]T: The sensations come back, of nostalgia. I mean, it's the emotions that come back up, nostalgia, anger, it's not the memory… The emotions, I mean the impotence.[I/T]M: What are you feeling now, the impotence?[→ I/T]T: Yes. [I/T]M: Is that what you couldn't get a handle on? [→ I/C]T: Yes, exactly maybe the impotence of not having - I as I do generally - I mean that I let things go rather than assert myself on things, I don't assert myself on things … Because I don't want to get to a discussion… [I/C]Like when S. says to me “Oh, the dog's staying with me, because I can provide it with more things”… [Aw/C]M: And you want that dog?[→ I/C]T: Yes, I want it [I/C], but I can't, I made this choice [D/C]…M: …Yes, yes… on a cognitive level it seems very clear: “I chose this”.T: Ok, on an emotional level. Ah no, because clearly it wasn't good for me.M: And that thing there comes and returns, cyclically [→ I/C].T: …now I am starting to reason in a much more selfish way [Aw/C]M: [the patient talks about how recently she is feeling the necessity to assert herself in various contexts] …Ah there you are, if you could think in a selfish way when you're with L?[→ I/C]T: Ah I'd like to give him a slap it's different [I/C]…but there as well, what's the point of it…?[D/C]M: There's the sense of listening to what you feel. That's it, what you feel. As a fantasy, if you could what would you do to this L?[→ I/C]T: Ah, I'd gladly give him a few slaps [I/C]M: …[the patient stimulated by the therapist expresses her anger through the use of fantasies]You knocked it down, and you knocked it down, and you knocked it down… and now, luckily, it's coming up, it's coming up, it's coming up…T: I had enough…That strength I… I've always had it inside.[Aw/P]M: Very good, meanwhile let's try to understand what there is underneath it, that reservoir that stayed there and let's start to knock it out, and to process it…Have you seen that we've caught our fish: you are very angry with him still … Can you accept it?T: Yes![Aw/T]M: In the therapy extract, we can observe some elements that indicate a good level of ego strength in the case of Maria. First of all, it can be observed that anxiety is present at manageable levels and is mainly discharged at the level of the striated muscles . As typically happens with this type of manifestation of anxiety, the defenses are of an evolved type and concern the recognition of emotional aspects on a cognitive level with an avoidance of the actual emotion (the patient smiles while telling a sad episode so as not to come into contact completely with the sadness) or the repression . Finally, we see that Maria manages to understand the therapist's interventions without getting too anxious and easily acquires aspects of awareness.This excerpt is taken from the third session. The patient starts with an episode from his own past (P) in which he recounts a situation where he had been very frightened, and his fear had not been accepted sufficiently. The patient easily links the terror he felt in P with the terror he currently feels during his anxiety crisis (C). The therapist encourages Fabio to focus on his emotions in recalling that episode in the here-and-now of the session (T), helping the patient to recognize some defensive tendencies and to get in touch with his own impulses of sadness (I).I was on my way home and there was someone there, I met someone who was like, “Hey there, who are you?” Ah I got scared for a moment no, pretty scared for a child…Then this person I saw - then maybe I imagined - that he was following me from behind, so I had a moment and started running. [I/P]F: T: How scary![→ I/P]Oh yes quite so… there was nothing there, it was in the middle of nowhere, to get home, that is there are only fields and so I was alone there… And then I was like this [indicates a child's height], the other guy was like this [indicates an adult's height]… [I/P]F: T: And so you were very scared [→ I/P]F: Yes, exactly [I]T: And so every time you went that way, you relived that fear? [→ I/P]F: Yes pretty much [I]T: Have you ever had a chance to talk to anyone about that moment?… was your fear somehow acknowledged? [→ I/P]F: Yes, it was acknowledged, but I couldn't find a solution. So….T: Ok.My dad told me, he said, “Look, don't worry about it…” I mean, a reassurance that's a little too rational, that's all.F: He didn't listen to you. (he hugs his belly)T: F: Exactly.That kid was still worried [I/T].T: Yes, terrified [I/T]F: Terrified. By others?[→ I/C]T: Well, in this case yes, well now that you mention it this terror maybe with the panic attack comes back a bit when… for example in a deserted street like I told you… [I/C].F: Is this memory useful to you? I mean, this connection that you're making? [→ Aw]T:  Well, it's useful because I see a similarity between the terror felt in both cases. [I]F: …The terror of the child being left alone with maybe someone following him in the fields… … [I/P]T: Yes. (I/P)F: And terror of the adult who, on the other hand, how can I put it, connects, links up… …[→ Aw of the link between I/P and I/C]T: Yes.F: with the terror of the child. [Aw of the link between I/P and I/C]T: F: Because it is the same terror in those moments when the panic attack… in fact I feel like a child… I feel in the middle of the fields, lost, small… helpless even. [Aw]T: Small, helpless, scared.F: Scared.…Where are we now, out of these things? [→ I/T]T: in this moment, sadness [I/T]F: as if we had also evoked the sadness of when you were a child… That child was feeling so many things [→ I/T]T: …Yes, quite… I've always made things complicated. [D/T]F: You're judging yourself [→ D/T]T: Yeah, my parents told me I was complicating things [D/P]. And now I just remembered that around elementary school - these episodes are all around elementary school - I had to go… [D/T]F: Can I stop you for a moment? [→ Al]T: Yes. [Al]F: I think it's useful to stop, otherwise we'll move on to more cognitive aspects… [→ Al]. Remember that it' s all right, it's all right. [→ E]… But it's like we're jumping a little bit away from these emotions [→ D/T]T: Ah ok [Al]F: It's not a judgment, no one is to blame, it's okay. [→ E]. But I think it's useful for you to stay on these emotional issues that have emerged very clearly and very strongly [→ Al], otherwise there's a chance we'll do it the way we did it  [→ D/T]T: Oh, okay, I get it, yeah, you mean, just distance yourself right away… [Aw/T]F: Distance yourself immediately. Instead we found out that that child was angry, scared, feeling helpless [→ I/P]… Now you're feeling these emotions here [→ I/T]T: Ah [sigh] [A/T]F: Ah [sigh] [E/T]T: Ah, it's not simple…[A/T]F: It's not simple [E/T]. As far as I can stand them, how can I say this, I'm there, I'm with them, it's a way to be with that child too…we here maybe have the chance to be with that child. IfT: not, we'll leave him alone one more time. [→ Al].Ah ah, ok. Yes that's ok. [Al]F: Mm? Do you have it, are you seeing it?T: Yes.F: And what's it like?T: I don't know, I'm picturing him locked in a corner with some bars… crying. [I/T]F: Ah, ok. Mm. And as you see him, what can you do? Now, that you're older. [→ I/T]T: … [the therapist explores a possible Impulse]Well, I'd give him a hand and caress him, let's say… [I/T]F: Does he feel it? [→ I/T]T: Yes. [I/T]F: And how is he? [→ I/T]T: Ah, warmer, more relaxed [I/T]F: Listen to yourself for a second. Don't use words, there's no need to explain [→ I].T: Ok. [Silenzio] [I]F: Listen to yourself. How's your breathing, how's your body, how is this sensation of warmth? [→ I]T: Calmer, more relaxed. With fewer things running through my mind [I/T]F: Calmer, more relaxed. The warmth calms. [→ I/T]T: Yes. Ah yes, the thoughts as well. [Connects I and D]F: It calms your thoughts as well.T: Yes.F: So even the thought of that child with the hand calms you down.T: Ah yes. Pretty much, yes. But my ears are ringing [A/T]F: Yeah. Okay. All right. It's okay, it's okay. We're working on some important stuff… [E/T]T: Ah ok [E]F: So there is a realignment of your structure right now [→ Aw]. Do you follow me? [→ Al]T: Ah ok. Yes yes yes yes yes. Yes yes yes yes ….[A/T] F: Have your ears started ringing? [→ A/T]T: My ears have started ringing [A/T]F: Was there also a feeling of movement a little bit inside? I mean 'oops'! [→ A/T]T: Yes, exactly yes [Aw].F: You' re becoming aware of yourself in a different way from the way you were before, you're in contact with a part of yourself, emotionally and physically, as you weren't before…[→ Aw].T: …In this second therapy extract, we can observe certain elements that are indicative of a low level of ego strength in Fabio's case. It can be noted that the anxious manifestations also involve cognitive-perceptive aspects (ringing in the ears), as well as those concerning the striated muscles (being stuck to the chair) Abbass, . To dealvs. treatment phases, baseline vs. follow-up phases, and treatment vs. follow-up phases  of change in CORE-OM scores  from baseline mild range of distress. As shown in mild range to the healthy range of distress. Thus, CORE-OM scores show a complete recovery for Maria.Maria's CORE-OM scores at baseline were in the clinical range, except for the functioning score that was in the normal range , as well as in subscales well-being (ES = 2.44) and psychological problems (ES = 2.99). A large ES was found for the functioning subscale (ES = 1.28), and a medium ES was also observed for the risk subscale (ES = 0.75).This description was confirmed in statistical analysis. In “baseline vs. follow-up” comparison.Similarly, in “baseline vs. follow-up” comparisons, very large ESs were observed in CORE-OM total scores (ES = 2.88), in the well-being (ES = 4.03) and psychological problems subscales (ES = 1.01), and a large ES was observed in the functioning subscales (ES = 1.01). Only a small ES was found in the risk subscale (ES = 0.75) for the “baseline healthy to the low-level range of distress in the follow-up phase . In line with this description, non-relevant changes were observed in the “treatment vs. follow-up” comparisons, indicating the maintenance of achieved CORE-OM scores.The described improvements were maintained in follow-up evaluations, except for the risk subscale score that increased slightly in the last follow-up (6 months), influencing the global score of distress that moved from the low-level to the mild range of distress. A partial recovery of previous scores was achieved after the 18th session, but it remained in the mild range of distress.Although Fabio reported severe symptomatology and the therapists evaluated his personality as being low structured, Fabio's total scores compared with Italian normative data were within the nonclinical range at the beginning of the therapy. As shown in The peculiar evolution of this case was also reflected in the statistical evaluations see . In “basIn “baseline vs. follow-up” comparisons—which is less influenced by fluctuations in the score during the therapy—a large ES indicating improvement was observed for the well-being subscale (ES = 1.08). However, very large and large deteriorations in ES were observed, respectively, for the functioning (ES = −1.62) and risk subscales (ES = 1.23), whereas non-relevant changes were observed in the psychological problems subscale and in the CORE-OM global score.vs. follow-up” comparisons where a medium ES was obtained for the CORE-OM global score (ES = 0.57), the well-being subscale (ES = 0.84), and the psychological problems subscale (ES = 0.54), whereas a medium ES of deterioration was maintained for the risk subscale (ES = −0.54), and non-relevant changes were observed for the functioning subscale.The partial recovery achieved after the 18th session was maintained in follow-up evaluations. This recovery can be statistically observed in the “treatment Although quantitative data indicated a positive outcome for Maria and a negative outcome for Fabio, the qualitative evaluation of the psychotherapy outcome realized using the Change Interview method accounts for a very positive outcome for both patients. They reported several changes classified as very important and extremely important, and they considered many such changes as being unlikely without the therapy. Interestingly, most of the reported changes are in line with the declared aims of ITAP. They concern interpersonal relationships , emotion regulation , and the improvement of self-representations achieved through contact with self-relevant impulses. Detailed results of the Change Interview are reported in what works for whom approach, our final aim was to reflect on the possibility that intensive interventions may be differently efficacious in helping patients with different levels of psychic structure integration.In the present study, we contrasted two clinical cases of patients with different levels of ego strength (or different levels of psychic structure integration) treated with ITAP, a new psychotherapy approach that aims toward the intensification of therapist intervention through the integration between transactional analysis and brief psychodynamic approaches. Following the If we consider ITAP outcomes evaluated using quantitative measure, CORE-OM data account for clearly different outcomes in the clinical cases analyzed in the present study. Maria—the patient with a well-integrated psychic structure—obtained a complete recovery, with a rapid improvement in early sessions and the maintenance of these results in follow-up evaluations. This pattern of change corresponds to a typical trajectory of change previously described in the literature  for patients with less ego strength.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by Ethical Committee Psychology University of Padua (number 1703). The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.IM: study planning, data analysis, and manuscript writing. AM: process material preparation. FS and MS: therapy provision, study planning, and ITAP conceptualization. EB: study planning and realization of change interview. AG: manuscript revision and supervision. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Nature Communications 10.1038/s41467-021-24787-1, published online 22 July 2021.Correction to: The original version of the Source Data associated with this Article included an error in the sheet for Supplementary Figure 1, which contained two incorrect data points. The correct content of cell C15 is ‘2.0048’ instead of the original, incorrect ‘2.1224’ and the correct content of cell D37 is ‘4.5090’ instead of the original, incorrect ‘4.4090’. The HTML has been updated to include a corrected version of the Source Data.Updated Source Data


A dichotomy theorem for the complexity of deciding whether a graph has a 1-frugal colouring with k colours was found by McCormick and Thomas, and then later extended to restricted graph classes by Kratochvil and Siggers. We generalize the McCormick and Thomas theorem by proving a dichotomy theorem for the complexity of deciding whether a graph has a t-frugal colouring with k colours, for all pairs of positive integers t and k. We also generalize bounds of Lih et al. for the number of colours needed in a 1-frugal colouring of a given t-frugal colourings, for any positive integer t.A  G is t -frugal if, for every c, the colour c is assigned to at most t vertices of N(v). We consider only proper colourings.A colouring of a graph G with sufficiently large maximum degree has a Frugal colourings were introduced by Hind, Molloy, and Reed in 1997 . Their molouring . Their wolouring .t for which a graph has a t-frugal colouring with a given number of colours, we fix t and focus on the number of colours needed for a t-frugal colouring. The t -frugal chromatic number of G is the smallest positive integer k, such that there exists a t-frugal k-colouring of G, and is denoted by Rather than focussing on the values of t-frugal colourings of planar graphs and outerplanar graphs. For planar graphs, they showed Amini, Esperet, and van den Heuvel  examinedinjective colouring, distance 2 colouring, colouring the square, and L-labelling; for example, see [G is G by adding edges between all pairs of vertices at distance 2 in G.The case ple, see , 12, 26.ple, see . Similarple, see , pages 1G is planar, then:G is a Wegner  conjectu settled , 25. In vatipour  establisand Reed  later shh et al.  proved aG be a Let The proof of this theorem appears in Sect. k-colouring. Their result was later strengthened by Kratochvíl and Siggers [k-colouring [k-colouring is NP-complete. By contrast, it follows from Brooks’ Theorem (applied to the square) that any graph with maximum degree at most k-colouring.McCormick and Thomas  determin Siggers . The proows from . The proolouring . Kratocht and k by proving:We generalize the theorem of McCormick and Thomas  to all pt-frugal k-colouring is solvable in polynomial time. If t-frugal k-colouring is NP-complete.If The proof of this theorem appears in Sect. t and k, the existence of a t-frugal k-colouring can be described in monadic second-order logic. Hence, by Courcelle’s Theorem [For all integers  Theorem , the exid must be assigned different colours are discussed in [L-labellings, which generalize L-labellings, are surveyed in [We conclude this section by briefly mentioning some related work. Locally injective colourings which need not be proper colourings are considered, for example, in , 20, 28.ussed in , 27. Resveyed in , 6G is called G can be transformed into A graph t-frugal k-colouring can be decided in linear time for graphs of bounded treewidth, hence in particular for t-frugal chromatic number of a n vertices. However, since t-frugal chromatic number can be computed in linear time [As noted in the previous section, the existence of a entclass1pt{minimaear time .In this section, we prove Theorem G be a u be a vertex of G. Let Let G be a there exist two adjacent vertices of degree 2;u with there exists a vertex  Let G beUsing this lemma, we now prove Theorem The case h et al. . Hence, G is a proper t-frugal colouring of G. Since If For convenience, let:G by induction on G be a n vertices. Our strategy is to delete a vertex w to obtain H can be coloured by induction. We then seek to extend the colouring of H to G by assigning a colour to w. We will show that the number of colours which are excluded as options for the colour of w is less than the number of colours which are available; hence, an extension exists. For a vertex w in G, let t-frugal colouring of H to a proper t-frugal colouring of G. Colours are excluded if they are used to colour a vertex adjacent to w, or are used t times in the neighbourhood of some neighbour of w. Therefore, w in G.We colour w be a vertex with degree 1. Clearly, H can be t-frugally coloured with t-frugal colouring of H can be extended to a t-frugal colouring of G.Suppose first that v and w, such that H can be coloured using w and v have degree 2, and w can violate the frugality condition for v. Therefore, the neighbour of v at distance 2 from w can be disregarded which leads to the slightly improved bound H can therefore be extended to a t-frugal colouring of G.Next, suppose that there are vertices u, such that u and x, and let By Lemma x contains the neighbourhood of u, because no two vertices of degree two are adjacent and x is the only possible neighbour of u which does not have degree two. (Note that u and x are not necessarily adjacent.) Since H with x contains the neighbourhood of u, we have H can therefore be extended to a t-frugal colouring of G.Suppose that H is t-frugally coloured using x and y to u.Suppose that H can therefore be extended to a t-frugal colouring of G.First, suppose that c be a t-frugal colouring of Now, suppose that u is not adjacent to a vertex with colour c(x), then either u can be recoloured, so that c can therefore be extended to a t-frugal colouring of G.If u is adjacent to a vertex with colour c(x), then we have:c can therefore be extended to a t-frugal colouring of G.If Finally, suppose that This completes the proof. P-colouring is formally defined as follows.The decision problem Problem:P-colouring, Instance: A graph G.Question: Is there a proper t-frugal k-colouring of G?P-colouring clearly belongs to NP for all integers P-colouring for each NP-completeness of d Thomas  .P-colouring, for all pairs of positive integers t and k. We first treat some special cases, and then derive the general result from them.We will extend the result to P-colouring is NP-complete.The transformation is from 3-colouring.G be an instance of 3-colouring. We construct an instance P-colouring from G as follows. First, consider the graph H with vertices x, y, and z, such that x is adjacent to y, and the vertices y and z are connected by three paths of length two. For each H as follows. For each vertex u, such that H in which the vertices x, y, and z of H, respectively. Let Let mentclass2pt{minimv, ordered arbitrarily.As above, let Claim 1: In a 2-frugal 3-colouring of the vertices for must receive the same colour.It is sufficient to show that We refer to the colour used to colour the vertices Claim 2: can be coloured, such that, forand use different colours.i, i is even, and colour 3 when i is an odd. Then, since Without loss of generality, we may assume that the colour of Claim 3: Ifuandvare adjacent inG, then the colour of is different than the colour of By construction, c of G is given. To extend this to a 2-frugal 3-colouring c(v) be the colour of c is a proper colouring, and from Claim 3. Therefore, Suppose a 3-colouring c of G from c(v) be the colour of c will assign different colours to u and v. Therefore, c is a proper 3-colouring of G.Finally, suppose a 2-frugal 3-colouring P-colouring is NP-complete. Therefore G be a graph. The corona ofG with respect toG by, for each vertex v of G, creating a copy of v is adjacent to each vertex of its copy of Let P-colouring polynomially transforms to Let G be an instance of P-colouring. The instance of G is the graph H which is the corona of G with respect to G has a t-frugal k-colouring if and only if H has a k-colouring.Let c of G, a colour x, and a vertex c that the colour x appears in the neighbourhood of v.For a colouring c be a t-frugal k-colouring of G. Clearly, c can be extended to a proper colouring H by, for each v using each of the x appears in the neighbourhood of v is exactly c is t-frugal, we have k-colouring of H.Let k-colouring of H. We claim that the colouring c of G induced by t-frugal k-colouring. To see this, observe that for every x must be used exactly once in H associated with v. Since c is a t-frugal k-colouring of G.Now, let We can now prove Theorem 1.2.P-coloured if and only if it contains no edges. If P-coloured if and only if it is bipartite with t. If t using Lemma If d Thomas  and indu


Under the assumption that covalent bonds are rigid, it is possible to compare the estimations of rigidity based on anisotropic and isotropic B-factors. This is done by computing the difference of the mean-square displacements (Delta-u) of atoms A and Z along the covalent bond A–Z, which must be close to zero for a rigid bond. The analysis of a high-quality set of protein structures, refined at a resolution better than  0.8 Angstroms, showed that Delta-u is significantly close to zero when anisotropic B-factors are used, with an average 60% Delta-u reduction. This reduction is larger for larger B-factors and this suggests that care should be taken in data-mining procedures that involve isotropic B-factors, especially at lower resolution, when anisotropic B-factors cannot be determined and when the average B-factor increases.The online version contains supplementary material available at 10.1007/s00726-021-02985-x. The benefits of high-resolution macromolecular crystal structures have been repeatedly described  are available, the mean-square displacement (u) of an atom is the same in all directions around the atomic average position, and the rigidity of the bond A–Z can be monitored by the function BA and BZ are the B-factors of atoms A and Z). With anisotropic B-factors (U), the Delta-u function must consider that the mean-square displacement (u) of an atom is not the same in all directions, and it must be computed as:which must be close to 0 Å, according to the Hirshfeld rigidity test : on average, it is 0.0108 (0.0001) Å smaller. This difference is larger for side-chain bonds [0.0157 (0.0002) Å] than for main-chain bond [0.0061 (0.0002) Å]. Only for 13% of the bonds, the isotropic Delta-u is slightly smaller than the anisotropic Delta-u and most of these cases concern the C–N backbone bonds. This percentage is smaller for side-chain bonds (10%) than for backbone bonds (17%).In general, and as expected, anisotropic This is certainly not surprising. In fact, given the assumption that covalent bonds are rigid, this reflects the better modeling of atomic dispersion around the equilibrium positions in anisotropic refinements. In other words, the rigidity of covalent bonds is better accounted for by anisotropic B-factors refinements, especially for side-chains, which tend to be more flexible.Delta-u are equal, on average, to 0.0075 (0.0001) and 0.0184 (0.0001) Å, the deviation from rigidity of the covalent bonds is reduced by 60% when anisotropic B-factors are refined. This improvement is remarkable and somehow surprising by its amount.However, the added value of the work presented here is the fact that this is a quantitative comparison, which points out that, given that the anisotropic and isotropic Delta-u shown in Fig. Delta-u increases considerably, from values close to 0 Å up to 0.04 Å, the anisotropic Delta-u increases much less, only from 0.006 to 0.007 Å to about 0.01 Å. This confirms that the covalent bond rigidity is drastically better monitored by anisotropic B-factors.This can be appreciated also by the relationship between the anisotropic and isotropic Delta-u tend to be larger for atom pairs that have a larger average isotropic B-factor Below is the link to the electronic supplementary material.


Nature Communications 10.1038/s41467-020-16601-1, published online 1 June 2020.Correction to: The original version of this Article contained an error in Figure 2, where the horizontal axis value ‘1600’ in panel (a) was incorrectly labelled as ‘1200’. This has now been corrected in both the PDF and HTML versions of the Article.


In the original article, there were errors. A correction has been made to:The legend in was–14.96 percentage points higher among the poorest mothers than among the richest mothers”, it should actually say “In 1993, the SII was–14.96, i.e., the prevalence of the outcome was 14.96 percentage points higher among the poorest mothers than among the richest mothers”.Also, in the presentation of the results of Table 3, a minus sign is wrongly placed. Where it reads: “In 1993, the SII was–14.96, i.e., the prevalence of the outcome I apologize for these mistakes on behalf of all co-authors.


Communications Biology 10.1038/s42003-021-02145-7, published online 10 June 2021.Correction to: y axis was titled, “Change from 1600 (%)”. The correct y axis title is “Change from 1600 ”. The correct version of Fig. 2 is:The original version of this Article contained an error in Fig. 2, in which the which replaces the previous incorrect version:y axis was titled, “Change from 1600 (%)”. The correct y axis title is “Change from 1600 ”. The correct version of Fig. 3 is:The original version of this Article also contained an error in Fig. 3, in which the which replaces the previous incorrect version:Both errors have now been corrected in the HTML and PDF versions of the Article.


The application of intermaxillary traction is often accompanied by the unexpected movement of dentition, especially anchorage teeth. The aim of this study was to comprehensively compare the influence of cross-sectional shape of ribbon arch wires with edgewise and round wires on intermaxillary traction in Class II malocclusion treatment using FEA simulation.The dentofacial structure was simulated in finite element software. A retraction force of 1.5 N was applied to different cross-sectional orthodontic arch wires: a ribbon wire (0.025 × 0.017-in. and 0.025 × 0.019-in.), a rectangular wire (0.017 × 0.025-in. and 0.019 × 0.025-in.) and a round wire (Φ 0.018-in. and Φ 0.020-in.).Among the three groups, ribbon wire (0.025 × 0.017-in. and 0.025 × 0.019-in.) exhibited the lowest displacement in the X-axis  and Z-axis . However, the 0.025 × 0.017-in. ribbon wire showed the highest Y-axis displacement. In the round wire group, Φ 0.020-in. wire displayed less rotation than Φ 0.018-in. wire, where the sagittal, frontal and occlusal rotation of Φ 0.020-in. wire was almost half of that of Φ 0.018-in. wire. The movement of the first molar region was intermediate between the ribbon arch group and the round wire group. Notably, the values of the 0.025 × 0.017-in. arch wire displacement, which were higher than those of any other group, peaked at 0.019 mm in the central incisor region with a spike-like shape. The deformation range of the Φ 0.018-in. wire group was the largest in this study.The cross-section of the arch wire influenced force delivery in Class II intermaxillary traction. With the same shape, a larger cross-sectional area led to less mandibular dentition movement. For the rectangular arch wire and ribbon arch wire groups, since the height and width were inverted, the vertical displacement of anchorage teeth in the ribbon wire group was reduced, but the possibility of buccal tipping in mandibular anterior teeth also increased. Class II malocclusion, which is associated with a convex soft tissue profile caused by either mandibular retrognathism or excessive growth of maxilla, constitutes a significant diagnostic percentage of the patients seeking orthodontic treatment –4. AmongPrevious studies have characterized the geometry and size effects of orthodontic arch wires on the ultimate orthodontic treatment outcomes , 9. BracCompared with contemporary edgewise wires, the cross-section of ribbon arch wires represents an inversion of height and width. Historically, the ribbon arch, the first orthodontic appliance coupled with brackets, was considered the progenitor of edgewise appliances and earned popularity in the 1920s . The utiIn addition, there is a paucity of data from investigations into the role that the cross-sectional shape plays in maxillomandibular traction. The reason for this lack of data could be the great challenge in identifying tooth movement and deformation under the coexistence of sophisticated anatomical structures and various orthodontic elements . Finite The aim of this study was to comprehensively compare the influence of the cross-sectional shape of ribbon arch wires with edgewise and round wires on intermaxillary traction in Class II malocclusion treatment using FEA simulation.The study protocol was designed in compliance with the Helsinki Declaration and approved by the ethical committee of the Fujian Medical University Union Hospital. Through medical history interviewing and oral examination, a 20-year-old healthy male volunteer with a healthy craniofacial structure and complete dentition with normal crown root ratio and a normal occlusion, was selected for this study. Before inclusion in this study, this volunteer signed an informed consent form.The finite element (FE) model was based on the computed tomography  data, which referred to the sectional images of the volunteer from the upper rim of the condyle to the lower edge of the mandible in digital imaging and communications in medicine (DICOM) format. The CT data were collected and imported to the processing software  to further obtain a virtual model of the maxilla and mandible in Geomagic Studio . Along with the outer surface of the mandible, the periodontal ligament (PDL) was constructed at 0.25 mm thickness. The central area of alveolar bone was cancellous bone surrounded by 1.5 mm thick cortical bone.Rectangular wire  and round wire  were scanned and these scans were entered into software . Using the same method, the matching brackets, buccal tubes and slots were modelled virtually. The ribbon wire (0.025 × 0.017-in. and 0.025 × 0.019-in.) was constructed based on the rectangular wire with height and width inverted. The rectangular wires and round wires were coupled with a 0.022 × 0.028-in. slot, whereas the ribbon wire was inserted into the 0.028 × 0.022-in. slot, which was designed for the purpose of fitting the upright arch wire. An anterior hook of 2.5 mm height was built and positioned between the maxillary lateral incisor and canine while the tubes were placed in the first mandible molar and second premolar. In addition, stainless steel ligature wires were tied to the brackets from the second premolar of the mandible right to the left second premolar. Those orthodontic appliances were assembled appropriately on the buccal side of dentition and are shown in Fig. A nonlinear elastic finite element analysis was performed in Ansys Workbench 15.0 . The Coulomb friction coefficient between the ligature and brackets was assumed to be 0.2 with reference to other experimental data. Each anatomical component and orthodontic appliance was simulated with ten-node tetrahedral elements and assumed to have isotropic homogenous linear elastic characteristics. The sizes of the elements in the PDL, tooth and bone were set as 0.5 mm, 1 mm and 2 mm, respectively, in order to simplify the finite element model, which included both small element size in the PDL and a large volume of the bone and the teeth. The FE model with different arch wires consisted of 616,006–650,197 nodes and 321,732–325,321 elements in total while the numbers of nodes/elements were 56,376/30,327 for teeth, 243,141/120,459 for the PDL, 199,834/111,827 for bone and 116,655–150,846/58,534–67,280 for the remaining components, including tubes, brackets and different arch wires. Young’s modulus and Poisson’s ratio of cortical bone, cancellous bone, teeth, PDL, arch wires, brackets and tubes were determined from previous studies –23 and aA traction force of 1.5 N was applied from the maxilla anterior hook between the canine and lateral incisor to the hook of buccal tubes in the mandible first molar. The application of retraction force would initiate the movement of teeth, which could be defined by the displacement rotation of teeth, and the stress redistribution of the PDL. All the movement was suppressed for the nodes located in the bottom of the mandible segment.There were two coordinate systems utilized in this study. For a single tooth, the x-axis, was referred to the mesio-distal direction , the y-axis referred to the buccal–lingual direction  and the z-axis to the vertical direction . For other large volume components , the displacement of teeth was recorded on the basis of a standard coordinate system with the x-axis as the anterior–posterior direction, the y-axis as the medial–lateral direction, and the z-axis as the superior–inferior direction, whereas the anterior, medial, and superior directions were defined as the + x, + y, and + z directions, respectively. Rotation movement was decomposed into three planes of motion , and the corresponding directions  were predetermined as positive.The buccal cusps of the mandibular posterior teeth and the edge of anterior teeth were lined virtually as buccal lines, while the lingual cusps of mandibular posterior teeth and the cingulum of anterior teeth were connected as lingual lines. The movement of the lingual line and buccal line was recorded.The results of 46 teeth in terms of force component distribution, displacement and rotation movements in three directions are shown in Table For the rectangular wire group, with increasing wire size, there was a descending trend in the displacement in the Y-axis and Z-axis. The displacement of the 0.017 × 0.025-in. wire in the Z-axis direction was 9.17 μm and that of the 0.019 × 0.025-in. wire was 9.13 μm. Among the three groups, ribbon wire (0.025 × 0.017-in. and 0.025 × 0.019-in.) exhibited the lowest displacement in the X-axis  and Z-axis . However, the 0.025 × 0.017-in. ribbon wire showed the highest Y-axis displacement. The Φ 0.018-in. round wire also showed higher Z-axis displacement (9.44 μm) and Y-axis displacement (5.96 μm) than Φ 0.020-in. round wire .In the rectangular wire group and ribbon wire group, the rotation motion for 46 teeth in the sagittal, frontal and occlusal planes was − 0.002°, 0.020°, and 0.021°, respectively. In the ribbon wire group, the frontal rotation was higher than that in the rectangular and round wire groups, especially the 0.025 × 0.017-in. group, which exhibited 0.042° of rotation. In the round wire group, Φ 0.020-in. wire displayed less rotation than Φ 0.018-in. wire, where the sagittal, frontal and occlusal rotation of Φ 0.020-in. wire was almost half that of Φ 0.018-in. wire.Figure The detailed displacements  of mandible teeth after the application of 1.5 N retraction force is shown in Fig. The displacements of the buccal line and lingual line in different groups are shown in Fig. In the rectangular wire group (0.017 × 0.025-in. and 0.019 × 0.025-in.), the maximum displacements of the buccal line and lingual line were 15.98 μm and 15.91 μm, respectively. The movement of the first molar region was intermediate between the ribbon arch group and the round wire group. In the ribbon arch group, the lingual line displacement in the first molar region was 0.008 mm, which was also the lowest among the corresponding results of all the studied groups. Notably, the values of the 0.025 × 0.017-in. arch wire displacement, which were higher than those of any other group, peaked at 18.55 μm in the central incisor region with a spike-like shape. In the 0.025 × 0.019-in. group, the displacements ranged from the first molar to the central incisor of the buccal line, and the lingual line was lowest among the studied groups. In the round wire group, the displacement ranging from the first molar to the central incisor of the buccal line and lingual line was higher than those of the rectangular and ribbon arch groups. The movement induced by the Φ 0.020-in. wire was 16.11 μm, which was lower than that induced by the Φ 0.018-in. wire (17.18 μm).The deformation range between maximum deformation and minimum deformation in different groups after the application of 1.5 N retraction force is summarized in Fig. The high prevalence of Class II malocclusion in patients prompted the wide usage of intermaxillary elastic traction. However, scarce data and few documented details are available regarding the influence of arch wire geometry during the maxillomandibular traction procedure. In the present study, we principally aimed to simulate the dentofacial structure via FEA to explore the effect of arch wire cross-sectional shape on Class II intermaxillary traction.Often, the changes in vertical and horizontal vectors caused by Class II intermaxillary traction involve anchorage loss , 24, 25.I) of the rectangular wire is equal to “h3w/12” (where “h” refers to the height of the cross-section and “w” refers to the width); I of the round wire is equal to “πr4/64” (where “r” refers to the radius of the cross-section) [Based on the FEA model in this study, differential results were observed in the arch wire group with different cross-sections in terms of mandibular first molar movement. The mechanics of arch wires have been recognized as one of the contributing factors of anchorage loss but have not been fully investigated . Theoretsection) . When thsection) . In addiIn this FE study, the remarkable execution of the ribbon wire in minimizing the vertical and horizontal displacements provided the basis for reviving the ribbon wire. The good performance of the ribbon wire in anchorage control could be attributed to the relatively greater height of the arch wire cross-section. A greater height tended to enlarge the moment of inertia and provide more rigid support to the occlusal plane. To our knowledge, only Inami et al. reported a minimum vertical bowing effect with a ribbonwise lingual appliance . HoweverThere were very similar results displayed by different arch wire groups in which the PDL around the distal root endured the most stress. Previous studies also revealed the relatively high occurrence of root resorption in the distal root of the mandibular first molar in orthodontic treatment . In the The displacement results of the buccal line and lingual line as well as the displacements of mandibular dentition also demonstrated that there was an association between cross-sectional geometry and mandibular tooth movement in Class II intermaxillary traction. Monlasser et al. stated that the importance of the arch wire cross-section in mechano-therapy should be appreciated since the force level in the vertical direction was amplified from 16 to 120% when the 0.014-in. arch was replaced by the 0.016-in. . In the Arch deformation is directly correlated with the resistance to sliding, and permanent wire deformation heavily encumbers tooth movement efficiency . From thThere were some limitations in this study because this experiment was conducted entirely using computer software. For instance, the setting of biological characteristics may differ from the real properties in vivo. Future studies, especially clinical trials, should be conducted to investigate the effect of arch wire geometry in vivo.Within the limitations of this FEA, the cross-section of the arch wire exerted an influence on force delivery in Class II intermaxillary traction. With the same shape, a larger cross-sectional size led to smaller mandibular dentition movement. For the rectangular arch wire and ribbon arch wire groups, since the height and width were inverted, the vertical displacement of anchorage teeth in the ribbon wire group was reduced, but the possibility of buccal tipping of mandibular anterior teeth also increased.


Cell Death & DifferentiationCorrection to: 10.1038/s41418-020-00681-zhttps://www.nature.com/articles/s41418-020-00669-9) needs to be added to the start of paragraph 3, after ‘Hauck et al’. In addition, there was a typo in ‘Hauk et al’. The correct name is ‘Hauck et al’. The journal and authors apologize for the errors. The original article has been corrected.The original version of this article unfortunately contained an ommission in the references that occured in production. A reference to this paper (