The WD40 repeat (WDR) domain is one of the most abundant protein interaction domains in the human proteome. More than 360 protein interaction domains have been annotated thus far. The WDR domains mediate interactions with peptide regions of important interaction partners in a variety of biological processes. Proteins with the WDR domain which typically contains a seven-bladed β propeller, are continuously being discovered. They represent a large class of proteins that are likely to play important roles. WD40 repeat domain-containing protein 76 (WDR76) is a member of WDR domain-containing proteins. Although it remains poorly understood, it is potentially involved in DNA damage repair, apoptosis, cell cycle progression, and gene expression regulation. Ongoing research on WDR76 is increasing the knowledge regarding its basic functions and role in different pathophysiological. The study of WDR76 is challenging due to the complexity of its interactions with its partners. In the present review, we summarized the current knowledge regarding WDR76, its physiological functions, the close relationship with human diseases, and potential opportunities for target therapy. With the research development with WD40 repeat (WDR) domain-containing proteins, play vital roles in diverse biological processes. Typically, the WDR domain contains 4-8 repeating sequence units of 40-60 amino acids ending with a tryptophan-aspartate (WD) dipeptide . Thus faSaccharomyces. cerevisiae; it has exhibited histone affinity [WDR76 is a poorly characterized protein which is predicted to be a member of the WDR domain-containing superfamily . It was affinity . Moreoveaffinity , DNA metaffinity , promotiaffinity , etc. Thaffinity . Furtheraffinity , 15. Untaffinity  and coloaffinity .According to the currently available results, WDR76 is identified as a hub protein. However, the current understanding of WDR76 compared to other members of WDR domain-containing superfamily is very limited. Hence, the present review summarized the recent progress on WDR76 research with the aim to better understand the WDR76 protein and eventually lead to potential clinical target therapy in different diseases.Generally, the WDR domain contains a conserved serine-histidine and WD motif and it can retain its β propeller fold due to its structural adaptability . Each blSaccharomyces.cerevisiae for interactomes, is the fourth most abundant domain in the human proteome [The WDR domain, which is best characterized in proteome . Becauseproteome , 25. Forproteome , 27.Macaca mulatta. Moreover, they predicted the presence of a C-terminal WDR domain in all 17 homologues of WDR76 including human WDR76. Therefore, it appears that WDR76 is conserved in higher eukaryotes. Currently, the crystal structure of human WDR76 not been determined, Swiss Model [WDR76 is a poorly characterized member of the WDR domain-containing protein family. Recently, Dayebgadoh et al carried out a phylogenetic analysis on 17 different sequences of WDR76 homologues downloaded from the National Center for Biotechnology Information (NCBI) . The resss Model , a web-bss Model .https://string-db.org) [Similar to a large number of members of the WDR domain-containing protein family, WDR domain-containing proteins may present their specific functions through sequences outside the WDR domain. Thus far, limited research evidence suggested that WDR76 participates in several interaction processes, such as the protein-protein interaction (PPI) network showed in -db.org) . HoweverMUS-30), a nuclear protein, increased following DNA damage [mus-30 strains. In addition, the MUS-30-WDR76 interaction was shown to be functionally important in DNA damage repair.Spruijit et al found that WDR76 preferentially binds to 5-hydroxymethylcytosine (5hmC) than to cytosine (C). Purified WDR76 was treated as a green fluorescent protein (GFP) fusion protein and was found to interact with OCR, HELLS, and gigaxonin (GAN) . OCR, SpA damage . DeletioWDR76Δ) and the N-terminal deletion of WDR76 (WDR76Δ’)[WDR76Δ lost the ability to interact with the CCT complex, and WDR76Δ’ showed a significance decrease of WDR76 interaction with SIRT1, GAN, histones, protein kinase, DNA-activated, catalytic subunit (PRKDC), XRCC5, XRCC6, and PARP1. These results indicated that WDR76 interacted with partners via different regions instead of the WDR domain only.Gilmore et al focused on the interaction network of WDR76 and its recruitment to laser induced DNA damage . The res(WDR76Δ’). FurtherThe currently available evidence underlines the challenges faced by researchers in studying the WDR76 protein due to its complex interactions covering a diverse series of biological pathways. Proteins involved in the PPI map require further study to clarify the role of WDR76.The CUL4-DDB1- regulator of cullins 1 (CUL4-DDB1-ROC1) complex belongs to the family culling-containing ubiquitin E3 ligases . PreviouDCAF8 E3 ligase complex to catalyze LSH polyubiquitination. In contrast, WDR76 suppressed DCAF8-targeted LSH ubiquitination and proteasomal degradation through competitive inhibition of holo-CUL4-DDB1-DCAF8-LSH complex formation instead of direct interaction with E3 complex components. Molecular action of WDR76 in suppressing LSH incorporation into a functional complex corresponded to the distinct ferroptosis in cancer cells. The opposing regulation of LSH stability by WDR76 and DCAF8 decreased DNA oxidation and overproduction of reactive oxygen species (ROS), which was a crucial process in epigenetic regulation of ferroptosis. Transcriptomic profiling further revealed that the DCAF8/WDR76/LSH axis may be a critical epigenetic modulator of ferroptosis.Through proteomic analysis, Huang et al identified two potential WDR domain-containing proteins, namely CUL4-associated factor 8 (DCAF8) and WDR76, as substrate receptors of CRL4 family E3 for ubiquitination . LymphoiRAS proteins  are small guanosine triphosphatases (GTPases), which play essential roles in various pathophysiological regulatory, including cell proliferation, transformation, and development . The RASThen another related study to explore the function of WDR76 regulating HRAS protein stability in high-fat diet (HFD)-induced obesity and hepatic steatosis . The resAdenomatous polyposis coli (APC) mutation is common in patients with CRC, with an approximately 90% occurrence rate. Through aberrant activation of the Wnt/β-catenin signaling pathway. K-RAS mutation with 40-50% occurrence rate in CRCs cannot result in CSC only by itself [Wdr76, the protein levels of RAS were increased by activating the Wnt/β-catenin pathway, thereby inducing significant crypt lengthening and hyper-proliferation. Apc mutation and Wdr76 knockout mice exhibited increases in both the number and the size of tumors in small intestine. Besides, the study demonstrated that WDR76 reduced RAS level through polyubiquitination-dependent proteasomal degradation with APC-mutant D-WT and D-MT cells, which are isogenic except for harboring wild-type and mutant K-RAS, respectively. On the contrary, loss of WDR76 in CRC increased the level of RAS through the activation of the Wnt/β-catenin signaling pathway. This result suggests that destabilization of RAS by WDR76 is a potential treatment method targeting CRC involving CSC activation.CRC is a stem cell disease that occurs when the intestinal stem cells (ISCs) evade regulation and give rise to cancer stem cells (CSCs) , 68. Wnty itself . Howevery itself . WDR76 hy itself . Researcy itself . In miceAlzheimer’s disease (AD) is a common disorder, and its incidence increases significantly with age . HoweverGreat progress has been achieved on research regarding the WDR domain-containing superfamily. An increasing number of members of this family are found to be involved in multiple biological processes of various diseases. WDR76 is considered a hub protein with a diverse array of more than 100 interactions were found. The results of relevant studies have indicated that it is closely linked to a variety of diseases, including different types of cancer. Based on the studies available, WDR76 is identified as a novel tumor suppressor and RAS activity can be controlled via regulating protein stability which further affect the tumorigenesis and metastasis in different cancer diseases. The process of RAS protein stability regulation is complex and involves multiple signaling pathways. Therefore, regulation of RAS at the level of protein stability by WDR76, which mediating polyubiquitination-dependent degradation of RAS, may be a new therapeutic strategy. However, further research is warranted to elucidate the complex mechanisms through which WDR76 functions. This approach may clarify related pathophysiological processes, potentially leading to the discovery of effective target treatments.


We observe the manifestation of this coupling in uncommon types of topological defects like magnetoelectric domain walls and vortex-like singularities.Magnetically induced ferroelectrics exhibit rigidly coupled magnetic and electric order. The ordering temperatures and spontaneous polarization of these multiferroics are notoriously low, however. Both properties can be much larger if magnetic and ferroelectric order occur independently, but the cost of this independence is that pronounced magnetoelectric interaction is no longer obvious. Using spatially resolved images of domains and density-functional theory, we show that in multiferroics with separately emerging magnetic and ferroelectric order, the microscopic magnetoelectric coupling can be intrinsically strong even though the macroscopic leading-order magnetoelectric effect is forbidden by symmetry. We show, taking hexagonal ErMnO 3, the linear magnetoelectric effect is symmetry forbidden. Here, the authors show a pronounced magnetoelectric coupling driven by superexchange interaction giving rise to types of topological defects like magnetoelectric domain walls and vortex-like singularities.In h-RMnO In the former case, magnetic and electric domains are one-to-one correlated, and every magnetic domain wall is a ferroelectric domain wall, too. This leads to potentially useful phenomena like control of magnetic domains by electric fields, and vice versa2. In contrast, in the latter case, the magnetic and ferroelectric domains and domain walls are not intrinsically linked to each other because of the independence of the associated order parameters. Magnetoelectric coupling phenomena may still be present, but they are not mandatory. The type-I multiferroic systems of hexagonal ferrites and manganites are model cases for such magnetoelectric coupling phenomena. In ferrites, it was shown that the leading-order, that is, linear magnetoelectric effect dominates the magnetoelectric coupling4. However, in the isostructural manganites, disregarding any magnetic-field-induced phases and rare-earth ordering5, the linear magnetoelectric effect is symmetry-forbidden6. The demonstration of strong magnetoelectric coupling phenomena in hexagonal manganites, despite this absence of the linear magnetoelectric effect, is at the heart of our work.The different interdependence of magnetic and electric order in multiferroics with jointly (‘type-II’) and separately (‘type-I’) emerging magnetic and ferroelectric order7 or within8 domain walls proposed earlier. It has significant consequences for the magnetoelectric domain morphology. We furthermore identify three types of magnetic domain walls with different types of magnetic pseudo-vortices at their meeting points. We thus see that the independence of magnetic and electric order in type-I multiferroics can lead to properties that are not open to type-II multiferroics and can thus be beneficial rather than detrimental to their magnetoelectric functionality.We show in experiment and theory that the superexchange interaction drives a pronounced microscopic magnetoelectric interaction. The associated bulk coupling phenomenon is distinctly different from the coupling between3 as representative of the RMnO3 family with R = Sc, Y, In, Dy–Lu is formed by layers of corner-sharing MnO5 bipyramids alternating with sheets of Er3+ ions. A phase transition from the non-polar P63/mmc to the polar P63cm space group occurs at TC ≈ 1430 K 9. It results from the collective tilting of every three neighbouring MnO5 trigonal bipyramids whose apical O2− ions jointly move along the radial direction relative to their central Er3+ site. The associated lattice mode has K3 symmetry and is parameterized by an amplitude Q and azimuthal rotation angle Φ, see Fig. 3+ ions along the c axis, giving rise to improper ferroelectricity with a polarization n × 60∘ , displaying ΔΦ = 60∘ and, hence, alternating polarization between neighbouring domains11. The system is famous for the formation of ferroelectric pseudo-vortices14, which arise due to the breaking of the effectively continuous symmetry of Φ close to the Curie temperature17.Hexagonal ErMnOTN = 77 K, the antiferromagnetic ordering of the Mn3+ spins occurs18 according to the magnetic K2 representation of the non-polar P63/mmc structure19. The spin angle between nearest Mn3+ neighbours in the basal ab planes is 120∘ with an arrangement of neighbouring planes along c as depicted in Fig. 3+ spins with the angle Ψ, where a change of Ψ corresponds to an in-phase rotation of all the spins in the ab plane, but with an opposite sense of rotation in the upper and lower half of the unit cell19. For Q = 0, we confirm, using density functional theory (DFT), that the energy of the magnetic order in Fig. Q ≠ 0, however, coupling of the magnetic mode to the structural mode described by a free-energy contribution∘.At 3+ sublattice is not affected by the distortive-ferroelectric transition10. Microscopically, however, a correlation between the spin and the polar lattice is established because the magnetic exchange between the Mn3+ ions, which determines the antiferromagnetic order, is mediated by the O2− ions21 whose displacement from their original high-symmetry positions is part of the of the structural distortion that leads to the ferroelectric order. Hence, the superexchange projects the polar order into the magnetic system3, thus establishing a bulk magnetoelectric coupling. It breaks the continuous symmetry in (Ψ − Φ) and centres the high-symmetry point of the magnetic lattice to that of the trimerized-polar lattice. The presence of this coupling is all the more striking as the linear magnetoelectric effect describing the emergence of a magnetization (electric polarization) proportional to an applied electric (magnetic) field is symmetry-forbidden in ErMnO36. In this aspect, the hexagonal manganites are strinkingly different from the hexagonal ferrites. In LuFeO3, the linear magnetoelectric effect is allowed and involves contributions from a magnetization of the Fe system along the hexagonal axis4, which is absent in ErMnO3.This constraint may appear surprising on first glance since the centrosymmetry of the Mn∘ or −90∘ in Fig. 3+ spins as sketched in Fig. 3. To date, there has been a single such investigation in the system of hexagonal manganites. Zero bulk magnetoelectric coupling was assumed23, and the peculiar vortex-like arrangement of the six associated domain states was not considered and could not be spatially resolved14.Symmetry analysis and DFT show that multiferroic structures with Ψ − Φ = +9025. ErMnO3 features two types of SHG contributions7, a ferroelectric one proportional to the electric polarization 24 allows us to distinguish domains with opposite signs of 26.We probe the spatial distribution of the domains by optical second-harmonic generation (SHG), yet with ten times higher optical resolution than in the earlier experiments (see ‘Methods’). SHG denotes the doubling of the frequency of a light wave in a material. It is a highly symmetry-sensitive process and can therefore distinguish between the different types of long-range order and domain statesc-oriented ErMnO3 sample (see ‘Methods’). First, the SHG light confirms the relation Ψ − Φ = ±90∘ derived from Eq.  immediately disproves the model of a piezomagnetic coupling between strained ferroelectric and locally magnetized antiferromagnetic domain walls proposed earliers, A > 0 are coefficients that we calculate from first principles (see ‘Methods’). As stated earlier, the second term is minimized by having Ψ − Φ = ±90∘ in each domain. The energy cost from the first term increases with the total rotation angle ΔΨ across the domain wall.The preservation of (Ψ − Φ) across the domain walls can be captured in the free energy by adding a gradient term describing the magnetic domain wall energy to Eq.  accordin∘ if Ψ tracks ΔΦ = ±60∘ across the wall; in this case both ∘ if only ∘ to satisfy Ψ − Φ = ±90∘ and is therefore also unfavourable.Regarding the change of Ψ across the domain wall we have the following possibilities. (i) ΔΨ = ±60∘, ∓120∘ or 180∘ in the same region of the sample after consecutive annealing cycles above TN. The microscopy images in Fig. We now investigate the occurrence of the three possible types of magnetic domain walls with ΔΨ = ±60∘ walls are most common and always appear at the same location because of their clamping to the ΔΦ = ±60∘ walls, which are not affected by the heating above TN. In Fig. ∘ wall. Even though ∘ wall across which the brightness of each antiferromagnetic domain is reversed. This is the only unclamped wall, across which only The energetically preferred ΔΨ = ±60∘ and ΔΦ = ±60∘ coincide and therefore exhibit sixfold magnetic pseudo-vortices in both Ψ and ∘ wall and a ΔΨ = 180∘ wall can occur as an intersection, which establishes a fourfold magnetic pseudo-vortex in both Ψ and ∘ wall and a ΔΨ = 180∘ wall can occur as junction with a ΔΨ = ∓120∘ wall, which establishes a threefold pseudo-vortex in Ψ, but not in The coexistence of the three types of magnetic walls with the topologically protected network of ferroelectric vortex-like domains leads to additional magnetic pseudo-vortices. According to the analysis in Fig. t}L Fig. f. The met}L Fig. h. Alternt}L Fig. g.3 domains in phase-field simulations, based on our model free energy in Eq. . An optical parametric amplifier converts the emission to a photon energy of 1.23 eV and a pulse energy of about 30 μJ. A ×20 long-working-distance microscope objective is used to collect the SHG light emitted from the sample and project it onto a liquid-nitrogen-cooled Jobin Yvon Back Illuminated Deep Depletion CCD camera. Optical filters in the optical path suppress any unwanted frequency components.32. For the calculation of the magnetic energy landscape, we use U = 3 eV. In the Er3+ pseudopotential, the 4f electrons are treated as core electrons, and therefore rare-earth magnetism is neglected. We use a k-point mesh of 6 × 6 × 4 and a plane-wave cutoff energy of 800 eV. All the calculations include spin-orbit coupling. To calculate the energy landscape  is obtained by performing a least squares fit to calculated spin configurations. The gradient parameter EKS(k) is the Kohn–Sham energy for the structure with a magnetic order modulated with a wavevector k. Numerically this was done using the spin-spiral implementation in VASP. Normalizing the order parameter Q such that |Q| = 0 in the high-symmetry phase and |Q| = 1 in the ground state, we obtain the following parameters for Eq. (s = 742 meVÅ2 for the gradient parameter and A = 2.13 meV for the anisotropy parameter (per 30 atoms). We note that this is a simplified version of the free energy put forward by Artyukhin et al.11, including only magnetic configurations of the magnetic K2 representation. We also calculate the free-energy parameters for ErMnO3 using the full expression11:s = 742 meVÅ2, a = 0.027 meV, C+ = −1.05 meV, C− = 0.0023 meV (per 30 atoms).For our first-principles calculations, we use the PBEsol+U approximation of the exchange correlation potential as implemented in the VASP code11 to derive the Ginzburg–Landau (GL) equations33 for the structural and magnetic order parameters. We use the values given by Artyukhin for the couplings of Q, Φ and 1,2 to Φ and ψ2,1 (see Eq. (34, using a grid spacing h = 0.1 nm and a time step dt = 0.1. We simulate only one layer in the ab-plane using a square grid consisting of nx × ny = 1024 × 1024 points. This corresponds to a physical length of the simulated system of about 100 nm. Since the magnetic domain walls have an expected width on this order11, we have to decrease this value in our simulation to obtain realistic domain patterns. We achieve this by increasing the coupling parameter a in Eq. (Q and the phase Φ as well as the electric polarization 4 steps. We then iterate the spin angles ψ1,2 on top of this pattern for 104 steps, resulting in the domain pattern shown in Fig. We use the Landau expansion for the free energy Reporting Summary Further Information on research design is available in the Supplementary InformationPeer Review FileLasing Reporting Summary


Electromagnetic tracking (EMT) can partially replace X-ray guidance in minimally invasive procedures, reducing radiation in the OR. However, in this hybrid setting, EMT is disturbed by metallic distortion caused by the X-ray device. We plan to make hybrid navigation clinical reality to reduce radiation exposure for patients and surgeons, by compensating EMT error.Our online compensation strategy exploits cycle-consistent generative adversarial neural networks (CycleGAN). Positions are translated from various bedside environments to their bench equivalents, by adjusting their z-component. Domain-translated points are fine-tuned on the x–y plane to reduce error in the bench domain. We evaluate our compensation approach in a phantom experiment.Since the domain-translation approach maps distorted points to their laboratory equivalents, predictions are consistent among different C-arm environments. Error is successfully reduced in all evaluation environments. Our qualitative phantom experiment demonstrates that our approach generalizes well to an unseen C-arm environment.Adversarial, cycle-consistent training is an explicable, consistent and thus interpretable approach for online error compensation. Qualitative assessment of EMT error compensation gives a glimpse to the potential of our method for rotational error compensation.The online version contains supplementary material available at 10.1007/s11548-021-02324-1. In minimally invasive surgery, electromagnetic tracking (EMT) has the potential to partially replace continuous X-ray navigation , reducinonly once. Online compensation of EMT error can be realized by implementing data-driven models, which generalize among data from different environments. In previous works, we investigated learning-based online EMT compensation by employing a series of increasingly complex learning models .interpretable error compensation technique, which imposes two more constraints beyond mere error reduction: explicability and consistency. Firstly, predictions need to be explicable; that is we need to know why a certain point from C-arm domain is mapped to a specific compensated point. Otherwise, compensation results could be arbitrary and still fulfill topological constraints, giving a false sense of reliability.Despite giving increasingly better results, the interpretation of the failure modes for these complex models is a growing concern in learning literature . Our majconsistency among distorted environments. Consistency is important for online error compensation, where training data stem from environments with varying distortion characteristics. If output is inconsistent among input environments, changing distortion characteristics of the electromagnetic field  affect the coordinate frame of compensated points. Such changes jeopardize the X-ray-to-EMT registration, rendering our envisioned hybrid setting infeasible.Our second constraint is C, which is the domain of C-arm-distorted points from environments similar to bedside, to domain L, which is the bench domain with points collected in a distortion-free laboratory setting. Our approach is both explicable and consistent by design and thus more interpretable than our ANN [To impose these two constraints, we approach the problem as domain adaptation with cyclic-consistent generative adversarial networks (GANs) , 17. The our ANN  approach our ANN , it has Offline compensation methods, such as interpolation schemes or polynomial fits, are extensively described in the comprehensive reviews by Kindratenko et al.  and Franonline compensation framework is proposed by Sadjadi et al. in 2016 [An  in 2016 . Their ainconsistent behavior.Neural networks for error compensation are employed by Kindratenko et al. in 2005 . The autIn this paper, compensation is performed by translating individual points from C-arm to laboratory domain using generative adversarial neural networks (GANs). This adversarial domain adaptation approach is based on the CycleGAN  architecOur data-driven compensation approach uses measurements we acquired during our previous work  and was q denotes the system’s quality estimate and Similarly to various AC EMT systems, the DC-based trakSTAR provides a quality estimate with each measuring point, indicating the amount of metallic distortion. Each measuring point is constituted by In our phantom study , we place the sensor at different positions inside an acrylic glass phantom, manufactured at Universitätsklinikum Würzburg, Germany. The phantom resembles a human aorta in life size. A 3D-printed Lego adapter holds the sensor cable Fig.  in placeOur learning models are implemented in Python using the PyTorch  frameworexplicable.To fulfill the explicability constraints we identified for interpretable online error compensation, we modify a domain adaptation approach that is originally used for image translation tasks. Instead of translating between two image domains , our goal is to translate EMT measurements from the bedside  to the bench  domain. Since the objective of this translation task is intuitive, we expect this compensation to be In the following, we detail the modified domain adaptation architecture, the protocol and parameters we use for training. Subsequently, we describe how error in laboratory domain is compensated by a post-processing step, which uses a simple linear regression model.We employ cycle-consistent adversarial training for interpretable EMT compensation. Similar to the work of Zhu and Park et al. , we makevalid laboratory point. Ideally, both parties in this adversarial two-player game achieve the Nash equilibrium [Each of the two GANs consists of a generator network and a discriminator neural network. The generator receives an input point and generates a domain-adapted point, whereas the discriminator judges whether the generated point stems from the target domain. The generator’s objective is to trick the discriminator by generating points close to its target domain, given an input point from the original domain. For instance, ilibrium , 12.z, quality and orientation.Our two generator models  share an identical structure. Generators receive a arbitrary points in the laboratory domain, the generators do not alter the x and y positional components. We focus only on compensating the z component, since of all positional components, it is the most susceptible to error (for the trakSTAR system). Error in the x–y plane is compensated in a fine-tuning step further described in section “To ensure that points from C-arm domain are not translated to Our training protocol is similar to that of CycleGAN, but includes additional loss terms tailored to the problem of EMT error compensation. In particular, we compute the generator loss as weighted sum of individual penalties, which are described in the following:Adversarial LossCycle loss As described in the original CycleGAN paper [L to domain C and back to L  as a means of regularization. Compensation loss is computed as The total generator loss is Although neural networks are known to generalize well to unseen data, predictions made under a lack of knowledge are uncertain. Fortunately, this uncertainty can be approximated by training the same architecture multiple times, but initialized with different random seeds (deep ensembling ). ComputOur discriminator models have three layers each, with 16 nodes per layer. All layers use LeakyReLU activations with a leak of 0.2, except for the last layer, which is Sigmoid-activated. The discriminators are trained with soft labels  .The generators also have four layers each, with 16 nodes per layer. Similar to the discriminators, the generator’s layers use LeakyReLU activations, but with a leak of 0.01. The last layer uses linear activation.Generators and discriminators are optimized under the use of Adam optimizer  both witx, y, z, q).As the cycle-consistent GAN model does not affect the x and y components of input points, there still exists positional error on the x–y plane. Assuming that the points compensated by ous work , using iWe first perform a bedside phantom evaluation of online error compensation. Afterward, we compare our domain adaptation approach to the ANN we have previously proposed .To assess the quality of our online compensation method in a realistic hybrid bedside setting, we combine EMT and X-ray imaging in a pilot phantom study. Figure The EMT sensor can be clearly distinguished from its background on the X-ray Fig. . We coulThe sensor tip is heading in positive direction of the tracker’s x-axis throughout the whole experiment. We expect azimuth angle to be constant and close to zero.Elevation is almost constant and near zero. Since the aortic phantom is slightly curved, elevation should decrease with higher x.Roll angle is hard to determine absolutely (only relatively). However, we know that it does not change substantially during the experiment, as the cable is not twisted and is rigidly attached to the Lego block.Figure Since our compensations alter rotation angles In Fig. On the other hand, topology-based compensation by our previously proposed ANN  does notAdversarial training with cycle consistency is beneficial for compensation performance, compared to training a single GAN translating C-arm to laboratory points. Vanilla GAN without cycle loss worsens overall compensation performance, as we show in Table Our fine-tuning step brings an additional boost in accuracy to the proposed CycleGAN setup Table . HoweverComparing our domain adaptation approach to previously proposed topology-based compensation , we see We train a modified CycleGAN on positions from various environments, achieving a translation of distorted (C-arm) to undistorted (laboratory) points. The CycleGAN-based setup is capable of reducing error in different unseen C-arm scenarios, while still producing consistent results. Since we can show that points are mapped to their correct laboratory counterparts—regardless of these being directly present in the training set—our approach is also explicable. Hence, our domain adaptation approach is interpretable by design.In this paper, we present an approach for online positional error compensation for EMT, which focuses on interpretability. Interpretable online error compensation raises trust in EMT, making it suitable for hybrid navigation, where the surgeon has to rely on EMT until the next X-ray image is taken. With reliable, online-compensated EMT navigation, radiation exposure can be reduced to a minimum, thus bringing less harm to patient and surgeon.Our cycle-consistent adversarial domain adaptation approach for EMT error compensation is interpretable by design and generalizes to unseen scenarios, as we demonstrate in a prototype hybrid scenario. As our method was originally designed to only compensate positional error, it is surprising to see that it has potential to correct rotational inaccuracies as well. However, specialized measuring standards need to be developed to verify the results on rotational error compensation. Further, we plan to investigate the applicability to other EMT devices, many of which feature a metallic distortion  estimate similar to the trakSTAR’s.In the future, we plan to investigate rotational compensation. Once our approach yields verifiable results on the rotational axes, it is ready for further bedside evaluations incorporating feedback of surgeons who use the hybrid system. Finally, more evaluations on the bedside bring us closer to make hybrid EMT navigation clinical reality.Supplementary material 1 (pdf 83 KB)Supplementary material 2 (mp4 77 KB)Below is the link to the electronic supplementary material.


We show that, by changing the dimensionality and the symmetries of the electronic system, coupling between structural and electronic properties prevents the universal behavior near the transition. By imaging the current flow in the system, we reveal that structural domain boundaries modify the filamentary flow close to the transition point, preventing a fractal with the expected universal dimension from forming.In systems near phase transitions, macroscopic properties often follow algebraic scaling laws, determined by the dimensionality and the underlying symmetries of the system. The emergence of such universal scaling implies that microscopic details are irrelevant. Here, we locally investigate the scaling properties of the metal-insulator transition at the LaAlO Macroscopic properties usually follow algebraic scaling laws near phase transitions. Here, the authors investigate the scaling properties of the metal‐insulator transition at the LaAlO3/SrTiO3 interface, finding that coupling between structural and electronic properties prevents the universal behavior. This property allows us to strip complex systems of their microscopic details and characterize them using only their dimensionality and underlying symmetries. For example, at a critical porosity, water percolating through the ground flows along a subdimensional fractal, whose dimension is independent of the soil’s details2. Fractals with the same universal dimension emerge in a variety of other systems, such as forest fires, galactic structures, and metal-insulator transitions3.Universal scaling laws in systems near phase transitions are one of the hallmark discoveries of twentieth century physics; near critical points, the thermodynamic properties of fundamentally different systems follow the same algebraic scaling laws5. However, the electronic transition is often intertwined with other material properties, such as magnetic and structural orders7. Although such couplings can change the dimensionality or symmetries of the electronic systems, it is unclear whether these orders interfere with the expected universal criticality11. Thus, to determine the mechanism driving the electronic transition, it is essential to resolve the interplay between the electronic and structural orders.Metal-insulator transitions in complex materials, like transition metal oxides, offer an experimental platform for testing the applicability of the universal scaling description. There are clear experimental observations of critical scaling consistent with percolation in a variety of transition metal oxides3/SrTiO3 (LAO/STO) interface. On the metallic side, the conductivity of LAO/STO is weakly modulated (in space) over structural domain patterns, which emerge from the STO substrate15. They lead to narrow, elongated, highly conducting channels, with lengths comparable to those of mesoscopic devices16. In LAO/STO, there is a gate tunable superconductor-insulator transition19. At higher temperatures, an MIT has been observed through resistivity22 and compressibility measurements23. Resistivity measurements revealed a percolation type transition21, but sample-to-sample variations near the critical point have been reported24.Investigating how domain patterns modify the electronic transition requires local tools, capable of both resolving the patterns, and discerning their effect on electronic properties. We therefore used scanning superconducting quantum interference device (SQUID) microscopy to image the current flow in proximity to the gate-tunable metal-insulator transition (MIT) at the LaAlOHere, we reveal that in the presence of domain boundaries, the critical behavior of LAO/STO is not universal. We show that metallicity persists along domain boundaries, as the bulk 2D system turns insulating. As a result, the current carrying backbone cannot scale with the expected universal fractal dimension. Using random resistor network simulations, we show that the lack of a universal backbone coexists with universal scaling of the conductivity, and that the conductivity threshold is size dependent. This combination of universal and non-universal properties suggests that transitions in complex materials must be probed over multiple length scales, to discern their true properties.G) is applied between the 2D interface, and a metallic surface at the bottom of the sample. Reducing VG pushed the sample toward its insulating phase. We first show that, in the absence of domain boundaries, the transition is locally consistent with percolation. In a mono-domain, on the metallic side, the current density was overall homogeneous, except for one local reduction . We studied metallic interfaces, with LAO thicknesses of 10 u.c. and 12 u.c. In such samples, a metal-insulator transition can be achieved by tuning the metallicity using electrostatic gating. We used a back-gate geometry, where a gate voltage 3, which is inconsistent with current paths that are one dimensional over a finite region. Thus, in a multi-domain system, the current carrying backbone cannot scale with the correct universal exponent.The current flow along the boundaries is inconsistent with the expected fractal structure: fractals scale sub-dimensionally with the system size (dG = 90 V) and close to the transition (VG = −66 V). The histograms transition from a narrow distribution, consistent with homogeneous conductivity in the metallic phase, to a wide distribution at VG = −66 V, which spans three decades of current density. We note that the current carrying backbone we observe is resolution limited, and may contain a finer structure. In this case, the maximal current density could be larger than the value extracted from the data, thus extending the low current tail of the histograms. We also considered the current distributions in different mono-domains, compared with that of the overall image. At VG = −66 V, histograms of different mono-domains vary with respect to the histogram of the overall image , confirming our samples have bulk characteristics of a gate tunable MIT. To see how a non-universal backbone can coexist with universal scaling of the resistivity, we used random resistor network (RRN) simulations. The simulations enable us to study how the critical behavior depends on the system size, a parameter not easily tuned in experiments. We show that, although conductivity can be rescaled with the correct critical exponents, the critical concentration strongly depends on the exact domain pattern, and the overall sample size. As a result, the transition is suppressed for macroscopic systems, and the critical scaling only occurs as a finite-size effect.Even though the current-carrying backbone we find here does not have the universal form expected from a percolation transition, previous resistivity measurements yielded the expected universal critical exponents27. This mono-domain network has a phase transition when the concentration of metallic nodes, 28. At pc, current only flows through a small portion of the metallic bonds, forming the expected subdimensional fractal. Correspondingly, the global conductivity of the network shows clear data collapse , and that the domain structure does not change with the applied gate. Thus, other than 30. We expect the detailed electronic properties to change the conductivity of the insulating phase. However, the current flow images show that the channels remain highly conductive even as the bulk turns insulating  limit. We simulated additional RRNs, with various system sizes and domain patterns  do not show the expected universal structure, whereas global features such as the conductivity scale correctly, at a size-dependent critical concentration, because the conductivity is determined by the largest mono-domain region. These results suggest that sample-to-sample variations observed in LAO/STO samples at low carrier densities (see Supplementary Note 10 for discussion) can be explained by variations in the domain patterns. Thus, studying the critical properties of mesoscopic systems requires probing them both on local and global scales.32 and host 1D superconductivity29, electric polarity13, and magnetic properties33. While the realization of such 1D devices requires better control over the size and orientations of domain boundaries, our results show how to decouple the 1D nanowire from the host 2D system.The lack of a fractal backbone also offers an opportunity to use the gate tunable MIT to study the electronic properties of individual domain boundaries. For example, orienting boundaries along the overall current flow could generate a 2D to 1D crossover, as the current will flow entirely along the boundaries. In STO, this is a particularly promising application, as domain boundaries support a variety of properties, not available in the bulk: they serve as 1D ballistic wave guidesTo conclude, we have shown that, near the MIT in LAO/STO, domain boundaries prevent onset of universal critical behavior. The boundaries hinder the formation of a universal fractal current carrying backbone, and modify the scaling behavior of the conductivity, by making the critical point size dependent. Our results suggest that when electronic properties are coupled to other orders, critical behavior depends on the finite-sized domain patterns, making it non-universal.7; MITs often occur together with a magnetic or structural phase transition39. To understand the electronic transitions, it is essential to determine how the structural/magnetic transitions contribute, and whether they are the driving force behind the MIT. These questions remain under debate40, because the structural and electronic properties are difficult to untangle. Our results suggest that, by modifying the filamentary flow, coupling between structural and electronic properties can create novel critical behavior. For example, near a structural transition, a metallic filament consisting of domain boundaries should be extremely susceptible to changes and can therefore strongly perturb the electronic transition.Coupling between electronic and lattice structures is characteristic of transition metal oxides44. Thus, engineering these couplings can generally lead to nanoscale control over the electronic properties and critical behavior of the films. This type of engineering could be a powerful tool for both fundamental and applied research. To achieve this, further work is required to improve the control over formation of domain patterns. Control over domain patterns (domain engineering) already has promising applications with ferroelectrics and ferromagnets45, and techniques established for ferroics could be applied to heterostructures.Our results also offer a generic platform for engineering the current flow in other oxide heterostructures. Through interface engineering, the domain patterns of the substrate can be imprinted onto the structure of thin films. Coupling between carriers in thin films and the structural properties or phonon modes of their substrates have been reported in a variety of heterostructuresFinally, we come back to the relationship between algebraic scaling and fractals. We showed that scaling exponents of global properties do not determine the fractal dimension on the microscopic scale. Our results therefore provide a counterexample to the hyper-scaling relations, suggesting that algebraic scaling of macroscopic quantities does not always imply self-similarity on the microscopic scale.2 terminated STO substrates, using pulsed laser deposition46. Growth conditions are described in Supplementary Table 1. The samples were patterned using an AlOx hard mask47. Electrical contacts to the sample were made by ultrasonic wire bonding directly to the interface. Alternating currents  were applied to the sample. The resulting magnetic flux was recorded with a scanning SQUID with a 1 µm pickup coil, using a lock-in amplifier. The current density was reconstructed using Fourier analysis48, and representative raw magnetic flux data are shown in the Supplementary Fig. S1. Data shown in Fig. LAO films were deposited on TiORRN simulations were performed on square lattice grids with dimensions D × D. Each node was assigned one of three labels: metal, insulator, or domain boundary. Metal and insulator labels were assigned randomly. Metallic nodes were given conductivity mentclass2pt{minimSupplementary InformationPeer Review File


Protein domain duplications are a major contributor to the functional diversification of protein families. These duplications can occur one at a time through single domain duplications, or as tandem duplications where several consecutive domains are duplicated together as part of a single evolutionary event. Existing methods for inferring domain-level evolutionary events are based on reconciling domain trees with gene trees. While some formulations consider multiple domain duplications, they do not explicitly model tandem duplications; this leads to inaccurate inference of which domains duplicated together over the course of evolution.Here, we introduce a reconciliation-based framework that considers the relative positions of domains within extant sequences. We use this information to uncover tandem domain duplications within the evolutionary history of these genes. We devise an integer linear programming approach that solves our problem exactly, and a heuristic approach that works well in practice. We perform extensive simulation studies to demonstrate that our approaches can accurately uncover single and tandem domain duplications, and additionally test our approach on a well-studied orthogroup where lineage-specific domain expansions exhibit varying and complex domain duplication patterns.https://github.com/Singh-Lab/TandemDuplications.Code is available on github at Bioinformatics online. Nearly all proteins contain short, modular subsequences known as domains. These domains have structural and functional properties, and can be categorized into domain families based on sequence similarity. The number of domains present in a protein varies widely, ranging from a single domain to over a hundred in some protein families  introduce a model for tandem duplication events, (ii) integrate this model into the reconciliation framework, (iii) give both an exact integer linear programming (ILP) solution and a significantly faster heuristic for the problem and (iv) show that we can accurately identify tandem duplications in both simulated and real data. We prove that our framework can correctly identify tandem duplications in the absence of domain shuffling and losses, and show in simulation that our methods are robust even under high loss scenarios.The rest of the article is organized as follows. Section 2 gives definitions useful for understanding our framework and defines the Tandem Duplication Loss (TDL) reconciliation problem. Section 3 gives our tandem duplication model and shows how to use the position of domains within modern day sequences to differentiate single and tandem duplications. Section 4 introduces our heuristic solution, while Section 5 demonstrates the performance of our methods on both real and simulated datasets.In this section, we give a description of the TDL reconciliation problem. We first introduce notation which will be useful in describing the problem, and then present our reconciliation formulation for finding multidomain duplications. We define tandem duplications, add constraints to distinguish between tandem and single duplications, and finally present a parsimony framework by which to optimize reconciliations. While we describe the reconciliation problem in terms of domain and gene trees, we note that it is equally applicable in the context of reconciling gene and species trees.G and the domain tree D, respectively. For any rooted full binary tree T, we denote the sets of vertices, internal vertices, leaves and edges by E(T), respectively. A directed edge, or arc, in T between parent node u and child v is denoted as . The parent of node v in tree T is denoted as u to v in tree T, we say that v is a descendant of u in the tree T , and we denote this by u and v are incomparable in T if T. We define the lowest common ancestor (LCA) of nodes x and y in tree T, termed v in T such that u where T when it is obvious. The distance between comparable vertices u and v in T, u to v if v and u in T. We denote the subtree of tree T rooted at internal node u as uT.Domain-gene reconciliation requires as input a rooted full binary gene tree and a rooted full binary domain tree. We refer to these phylogenies as the gene tree u in the domain tree).A leaf mapping γ, the full mapping from nodes in the domain tree to nodes in the gene tree. While inferring γ, a reconciliation also assigns an evolutionary event to each internal node in the domain tree. We consider three types of evolutionary events: co-duplications, tandem duplications and losses. Co-duplications are domain duplications that occur as a result of gene tree bifurcations, typically due to whole gene duplications or speciation events. Tandem duplications are duplications of one or more consecutive domains within a gene. To ensure that domains grouped together as taking part in the same duplication are actually part of a tandem duplication, we extend the typical reconciliation formulation to additionally use a pairwise eligibility matrix E. For any two nodes u and v in the domain tree, uvE = 1 if u and v could be part of the same tandem duplication, and 0 otherwise. Briefly, uvE is computed using the relative positions of the children of u and v on the gene. If their children are interleaved . We do not consider other possible evolutionary events (e.g. transfer of domains between contemporary sequences).Given domain and gene trees, the goal of reconciliation is to assign an evolutionary event to each internal node in the domain tree and pinpoint the gene in which it existed. To determine which ancestral gene a given domain was present in, reconciliation methods infer aved see , then u G, a domain tree D, a leaf mapping E, a TDL reconciliation consists of a full mapping D that are associated with co-duplications, and a set Δ where every tandem duplication is represented as the set of nodes in D corresponding to domains duplicated in that event. Note that within Δ, a duplication of a single domain u is represented as {u}, whereas a tandem duplication of domains I(D) is assigned either a co-duplication or a tandem duplication event. Every non-leaf domain node is assigned exactly one event, and therefore Σ and the sets contained in Δ together form a partition of I(D).More formally, given a gene tree G and D, mapping σ and eligibility matrix E, and thus γ, Σ and Δ are constrained. A valid TDL reconciliation is defined as follows:Definition 1Input: A full rooted binary gene tree G, a full rooted binary domain tree D, a leaf mapping and a symmetric, binary eligibility matrix E. Output: A full mapping , a set of co-duplication nodes and a set of tandem duplication sets such that:(TDL Reconciliation Problem). A TDL reconciliation must maintain biological consistency with the input trees For any s.t. For any where if and only if and are incomparable in GFor each  where i and xj are incomparable in Dx For any where and s.t. and d present in gene g may only be considered a co-duplication if the children of d are present in incomparable descendants of g. Otherwise, d is assigned a tandem duplication event. Conditions 3 and 4 constrain tandem duplication sets. Condition 3 states that for any pair of domains to be in a tandem duplication set, they must (i) have no ancestry relationship between the two, (ii) have been present in the same gene and (iii) be allowed to be in the same tandem duplication set by the eligibility matrix. Finally, condition 4 ensures temporal consistency between tandem duplication sets.These conditions combine our understanding of domain evolution with constraints implied by the inputs. The first set of constraints deal with domain to gene node mapping. A full mapping must respect the input leaf mapping. Because we do not allow horizontal domain transfers in our model, domains must follow the evolutionary history of their encompassing genes. If a domain is mapped to a particular gene, then its children must be mapped to that gene or descendants of that gene. The second rule is used to decide which event a domain is assigned. A domain G, there are no descendants of domain u observed in the other branch of the gene tree. We note that if u is a co-duplication node, G. An additional loss is inferred if u is part of a tandem duplication) and G, there is another loss that must have existed at node These constraints only pertain to tandem duplication and co-duplication events. Lost domains are not seen in existing genes and therefore do not show up in the input domain tree. Losses are instead inferred based on the mapping of domains to genes. For each parent–child pair Dc per set (regardless of size), while losses are assigned a cost Lc. The full cost of a TDL reconciliation is given byFor any input, there may be several valid reconciliations. We use a parsimony framework with event costs to choose the optimal one among them. Co-duplication events are required due to gene- or species-level events, and therefore have 0 cost. Tandem duplications are assigned a fixed cost Reconciliation has typically been used to infer gene-level events, with a few recent works extending the framework to domains. In the earliest reconcilation models, known as Duplication Loss (DL) models, duplications are restricted to consist of single domains (or genes), with a fixed cost for each duplication and each loss; these reconciliations can be defined using just the first two conditions of Definition 1, with no eligibility matrix input, and where each ear time  and Dondear time , more gek domains, iP be the position of domain i in a left to right ordering of domains on the protein, and assume without loss of generality that j and j + 1 are involved in duplication events, adding domains In a tandem domain duplication, one or more consecutive domains present in a single gene are duplicated at once. In order to correctly identify tandem duplications, we need to be able to differentiate between a tandem duplication of multiple domains and multiple individual duplication events. This requires knowing the relative positions of a set of domains and their copies post-duplication. Specifically, suppose a gene contains +1)′ see .Unfortunately, information on the relative ordering of ancestral domains is lost in domain phylogenies. In order to infer these, we make the following assumptions:k occurs, affecting domains with positions j is inserted at position j + k. Any domain previously at position l + k after the duplication.When a tandem duplication occurs, the duplication copy is inserted immediately after the original domains. If a tandem duplication of size iP < jP for domains i and j, then at no time point shall jP > iP. In the domain tree, this applies to all pairs of nodes i and j, and any of their descendants labeled with the same names . In the single gene case, we examine a domain tree Definition 3Let i and uj are pairwise eligible for allbe a set of two or more internal nodes in domain tree D. We say that X is tandem duplication eligible if u (Tandem Duplication Eligibility). Pairwise eligibility tells us whether two nodes could have been involved in a tandem duplication or not. Being pairwise eligible does not imply that two nodes were involved in a tandem duplication, but as we will see in the remainder of this section, in the absence of certain losses, two nodes that duplicate in tandem are guaranteed to be pairwise eligible. The notion of pairwise eligibility extends naturally from pairs of nodes to sets of nodes:Theorem 1.Let D be a domain tree containing all domains mapping to a single leaf gene. Let be a set of internal nodes in D corresponding to domains involved in a tandem duplication, and suppose no losses occur among their descendants. Then, under assumptions (1) and (2), is tandem duplication eligible.Like pairwise eligibility, sets of domains that underwent a tandem duplication event will be tandem duplication eligible in the absence of certain losses, but the converse is not necessarily true. We prove this in Theorem 1. Due to space considerations, all proofs are in the u be an internal node in domain tree D with children v and w, and g be a leaf in gene tree G. We say that g annotates u if vD and wD both contain domains occurring in g. A gene g annotates a pair of domain nodes u1 and u2. Any pair of internal nodes D may be annotated by zero, one or multiple genes. In each of these cases, we determine whether u1 and u2 are pairwise eligible as follows:In the multi-gene case, position values are no longer distinct. Each domain is assigned a position relative to other domains on the same gene, so domains appearing in different genes may have the same position value. The notion of pairwise eligibility is complicated by the fact that it is no longer clear whether two ancestral domains appear in the same gene without a mapping. Subtrees rooted at two internal domain nodes may not have any overlap in the genes that their leaves were present in. In these instances, we have no information on whether the domains at their root could be part of a tandem duplication. The key insight here is that we can only test tandem duplication eligibility between domains with descendants occurring in the same gene. Let u1 and u2 have no shared annotations, then we cannot determine the relative ordering of their children. That is, we cannot determine whether u1 and u2 are pairwise eligible, and so we are permissive and say that u1 and u2 are pairwise eligible.No annotations. If u1 and u2 have one shared annotation, then there exists some leaf gene g that annotates both u1 and u2. Let D formed from the leaves of D present in gene g; that is, D rooted at the least common ancestor of the domains of gene g. Note that u1 and u2 are both preserved in u1 and u2 are pairwise eligible if they are pairwise eligible in One annotation. If u1 and u2 are annotated by genes u1 and u2 are pairwise eligible if they are pairwise eligible in ig.Multiple annotations. Suppose tandem duplication eligible if iu and ju are pairwise eligible for all Theorem 2. Let D be a domain tree, and G be the containing gene tree. Let be a set of internal nodes in D mapped to gene node g in G corresponding to domains involved in a tandem duplication. Suppose there exists some such that no losses occur in the domain subtrees of rooted at . Then, under assumptions (1), (2) and (3), is tandem duplication eligible.See Theorem 3. Suppose nodes u and v in domain tree D are mapped to gene g and annotated by genes u and Dv. If u, v are marked as duplication nodes by the reconciliation framework and are pairwise eligible in, and no losses occur in their subtrees D i, then u1, u2 are pairwise eligible infor any g i.for all gTheorem 2 tells us that if a tandem domain duplication occurred, then the nodes in the domain tree representing those domains will be marked as pairwise eligible. Of course, the converse is not true; there may be some sets of nodes which are tandem duplication eligible but were not tandem duplications.Theorem 3 tells us that with no losses and under our assumptions, genes will not ‘disagree’; that is, if domains are ordered on one gene such that their ancestors could have been tandem duplications, assumption (2) tells us that sibling domains must be ordered the same way on any other gene as well. In cases where genes do disagree, either assumption (2) has been violated, or our domain tree is incorrect. In such cases, we do not constrain tandem duplication eligibility.n nodes, we define the n × n eligibility matrix E such that ijE = 1 if domains i and j are pairwise eligible, and 0 otherwise. Note that For a domain tree with u of our gene tree is taken from the leaf in its subtree with the minimum position value. If any other leaf in the subtree is lost, u will still be assigned the correct position value. Second, if a tandem domain duplication occurs in an ancestral gene g, then the descendants of those domains will be passed to all descendants of that gene. If no losses occur among those descendant domains in even one gene in L(g), our method will mark the domains involved in that duplication event as tandem duplication eligible . This problem can be solved in u1, u2.This mapping may be suboptimal for the full TDL reconciliation problem. However, as we show in Section 5.2, we find in simulation that this mapping tends to be very close to the ground truth mapping.R(g) be the set of all domains mapped to gene g. We find the sequence of tandem duplication events that minimizes the reconciliation parsimony cost for these nodes. This is done using a reduced ILP, given below, which is based on our full ILP  to allow for all possible tandem duplication sizes. ukT will be set to 1 if the length of the tandem duplication that node u belongs to is k, and 0 otherwise.ub term counting the number of nodes taking part in tandem duplication sets and the ukT term ensuring we do not double count tandem duplication events. The objective function omits the u is marked in a tandem duplication set with v, then v must also be in a set with u. Similarly, if u and v are part of a tandem duplication set, and v and w are also in a tandem duplication set, then u and w must also be part of the same set. Constraints 5 and 6 make sure that nodes are only part of tandem duplication sets if they are duplications to begin with, and that two domains may be part of the same tandem duplication set only if they are tandem duplication eligible. Constraints 7 and 8 ensure the T variables accurately count the size of tandem duplications, for the purpose of cost calculation. Finally, constraint 9 is the integer constraint on the X and T variables.Our reduced ILP is given below. Because there are no losses between domains mapped to the same gene, the objective function only needs to minimize the cost from tandem duplication events. This cost is given by R(g) is accurate, the tandem duplication events yielded by this process will be part of an optimal solution to the TDL reconciliation problem, and repeating this process on all nodes If u initially mapped to u could be mapped are ancestors of Once all domains are mapped and assigned events, we attempt to improve our solution by remapping domain nodes when doing so reduces the reconciliation cost. Note that our initial mapping was an LCA mapping. This means that for any domain node Let G, D and γ be a gene tree, domain tree and full mapping, respectively. Let such that . Let and and suppose . Then, at least losses can be saved by setting Lemma. This lemma tells us that the LCA mapping minimizes the number of losses inferred. Remapping a domain to an ancestor will increase the number of losses and therefore the overall cost of the reconciliation. The only case in which this is acceptable is if remapping a node can also decrease the number of tandem duplications we infer.X and Y, if X occurs after Y in the ordering. We note that if there exists such x and y, then there cannot exist nodes X occurring in gene g, we check whether every domain node in X can be remapped to an ancestor of g without violating any conditions in the definition of a TDL reconciliation. For any ancestor X can be remapped, we check whether X can be combined with an existing tandem duplication set already mapped to X to X to the node X originally mapped to gene g is remapped to an ancestor node g are still optimal. Similarly, because the number of tandem duplications in Remapping is done as follows. First, we create an ordering over tandem duplications sets such that for any two sets k occurring to be We tested our methods on both simulated and real datasets. Simulated data were generated using our TreeSim package, first described here , and witD between 0.1 and 0.01 to examine its effects on reconciliation accuracy. Large evolutionary event distances produce one or two events per gene, while low event distances can simulate a cascade of consecutive domain events within a single gene. We generate 50 gene and domain tree topologies at each of the five event distances, giving a total of 250 simulations. On average, we obtain 126, 83, 55, 29 and 17 leaf domains for event distances of 0.01, 0.025, 0.5, 0.75 and 0.1, respectively. For these event distances, respectively, we have on average 20, 7, 3, 1 and 0 domain losses, and 34, 18, 11, 5 and 2 tandem duplication events, of which roughly half affect two or more domains. All tests were performed using the trees generated by our simulation.Simulations were run using gene trees with eight leaf nodes and an average root to leaf distance of 0.3. We varied the mean distance between evolutionary events in We first test the accuracy of several methods that map domains to genes, as we need to use one of these as the mapping oracle for our heuristic. We test LCA mapping as well as the mapping output by a previous algorithm, MultRec  such that Pred of pairs of domains predicted to be part of the same tandem duplication. We create a similar set Real of pairs of domains that are actually part of the same tandem duplication in the simulation. Precision is computed as Next, we assess the ability of our full ILP, our heuristic and MultRec to infer tandem duplications. Each method is given the domain and sequence trees generated by a simulation, and our methods are additionally given an eligibility matrix, computed using these trees and the positions of domains in the generated extant sequences as described in Section 3. For each run of each of these algorithms, we compute precision, recall and F1 scores as follows. For every tandem duplication set We also report runtimes of our approaches. Each of the methods was run on a 3.2 GHz eight core Xeon processor with 64 GB of RAM. We used the gurobi  package Hirudo medicinalis and Trichoplax adhaerens, contain lineage-specific expansions in their filamin domain arrays. However, while the Filamin-A protein of T.adhaerens shows clear signs of tandem duplications, in H.medicinalis this protein appears to have increased its domain repertoire through repeated single domain duplications. We sought to recapitulate these results in a fully automated manner.Having shown that our heuristic works well in identifying tandem repeats on simulated data, we next apply it to a protein sequence family with numerous repeated domains. In particular, we used our heuristic to analyze the evolutionary history of filamin domains from the Filamin-A protein family. T.adhaerens while finding mainly single duplications in the lineage-specific expansion of H.medicinalis  the original domains, domain shuffling does not occur, and that losses do not occur to domains that were involved in a tandem duplication. We use this knowledge to constrain allowable tandem duplications found by reconciling domain and gene trees, and give both an exact ILP solution and a fast yet effective heuristic to infer these reconciliations. We note that our approach may allow tandem duplications consisting of sets of domains that are not adjacent to each other; this can occur when losses follow tandem duplications or there are errors in the input trees. Theoretically, it remains possible that using our method for determining whether domains can be part of the same tandem duplication, optimal solutions for TDL reconciliation may include tandem duplication sets consisting of non-contiguous domains even when evolutionary events occurred only under the assumptions of our model; however, we have not observed such an example. Despite these caveats, we show via extensive testing that the algorithms we develop significantly improve our ability to detect and distinguish between real tandem duplications and repeated single duplications. Moreover, we show the importance of this distinction using a protein family that exhibits both types of duplications in separate lineages.While we focused on three types of evolutionary events—co-duplications, tandem duplications and losses—other types of events, including horizontal domain transfers and domain merge/split events have been previously modeled. Adding these events to the TDL reconciliation framework will increase the accuracy of event inference in gene families where they occur. Modeling domain shuffling events, in which domains swap positions on the protein, would be particularly useful to our model as we rely on the inference of ancestral domain positions.With large protein families, or those with many domains, runtime can be an issue. This is especially important in families with tandem duplications, whose existence implies a large number of domains per protein. Our ILP solution, while exact, is unable to scale to realistically sized protein and domain trees. Our heuristic mitigates this issue, speeding up the process significantly while maintaining accuracy by running a simplified ILP on a series of smaller sub-problems. This approach scales to tens of proteins with dozens of domains, but has difficulty with protein families of interest such as the nebulin and immunoglobulin families, which can have over 100 domains per protein. Developing faster heuristics to assign tandem duplication sets would allow these families to be analyzed. Another challenge in inferring the evolutionary history of repeat domains within a protein family is that these domains can be quite short, with some containing as few as 20 amino acids. In these cases, it is difficult to obtain accurate phylogenies using traditional methods like RAxML. Recent methods such as TreeFix  [grant number R01-GM076275 to MS] and National Science Foundation (NSF) [grant number ABI-1458457 to MS]Conflict of Interest: none declared.btab329_Supplementary_DataClick here for additional data file.


The superiority of collaborative brain-computer interface (cBCI) in performance enhancement makes it an effective way to break through the performance bottleneck of the BCI-based dynamic visual target detection. However, the existing cBCIs focus on multi-mind information fusion with a static and unidirectional mode, lacking the information interaction and learning guidance among multiple agents. Here, we propose a novel cBCI framework to enhance the group detection performance of dynamic visual targets. Specifically, a mutual learning domain adaptation network (MLDANet) with information interaction, dynamic learning, and individual transferring abilities is developed as the core of the cBCI framework. MLDANet takes P3-sSDA network as individual network unit, introduces mutual learning strategy, and establishes a dynamic interactive learning mechanism between individual networks and collaborative decision-making at the neural decision level. The results indicate that the proposed MLDANet-cBCI framework can achieve the best group detection performance, and the mutual learning strategy can improve the detection ability of individual networks. In MLDANet-cBCI, the F1 scores of collaborative detection and individual network are 0.12 and 0.19 higher than those in the multi-classifier cBCI, respectively, when three minds collaborate. Thus, the proposed framework breaks through the traditional multi-mind collaborative mode and exhibits a superior group detection performance of dynamic visual targets, which is also of great significance for the practical application of multi-mind collaboration. Brain-computer interface (BCI) technology aims to build an interaction bridge between human and computer and provide a new technical means for the brain to control and monitor the external environment. Advanced BCI technology can not only help to improve the movement abilities of patients with physical disorders , 2, but The cBCIs are praised as one of the most promising applications in human augmentation –16. The Studies on multi-mind collaborative target detection have achieved remarkable results. However, some concerning issues remain. Firstly, in the current cBCIs, the computing models are static and unidirectional , 32–34 oThe MLDANet-cBCI framework was proposed for achieving better group detection performance. In particular, MLDANet establishes the information interaction and dynamic learning mechanism between individual networks and collaborative decision-making by introducing the mutual learning strategy at the neural decision layer.In the MLDANet-cBCI framework, the mutual learning strategy can effectively improve the individual network capability.In this study, we designed a novel multi-mind cBCI framework based on a mutual learning domain adaptation network (MLDANet), aiming at enhancing the group detection performance of dynamic visual targets. In the framework, a multi-mind synchronous cBCI experimental paradigm for UAV-video vehicle detection is designed; MLDANet is established where the P3-sSDA network is used as the individual network unit. This work made the following contributions.This collaborative brain-computer interface (cBCI) framework is designed to detect dynamic visual targets, as shown in 2) were transformed into black and white and reduced to 40% (768 × 432 px2) on the screen center against black background. In particular, the break duration totally depended on the subjects for sufficient relax. On average, the experimental duration time of 10 blocks (including break duration) was around 50 minutes for one participant.The experimental paradigm for vehicle detection from UAV videos, reported in our previous study , is depiA total of 89 healthy college participants volunteered for this study, with a median age of 25 years (right-handed), all of whom reported normal or corrected-to-normal vision and presented no neurological problems. They all signed the informed consent form before the experiment. All tests involving human participants were approved by the Ethics Committee of Henan Province People's Hospital.In this study, the EEG signals were collected by the g.USBamp  EEG recording with 16 electrodes. The electrode distribution followed the international 10–20 electrode location. The EEG online sampling rate was 600 Hz with band-pass filtering at 0.01–100 Hz and notch filtering at 50 Hz.The study was comprised of two parts: single-mind experiment and multi-mind experiment. 29 participants were recruited for the single-mind experiment, and each time only a single participant was invited to perform the detection task. The EEG signals collected from the single-mind experiment were used as the training set. In the multi-mind experiment, 20 groups (3 participants in each group) were recruited to perform the detection task together. The acquisition environment for the multi-mind synchronous experiment is shown in The parameter settings of data preprocessing were consistent between single-mind and multi-mind experiments. Firstly, using the fast ICA algorithm and EEGLAB toolbox, the electrooculogram was removed from the original signals. Next, data were filtered to 0.1–10 Hz and downsampled to 100 Hz. Then, target segments and nontarget segments were, respectively, extracted from target video-induced and nontarget video-induced EEG signals. The target trials were segmented starting from target onset time. One target video can only induce one target trial, and nontarget trials were segmented from nontarget video-induced signals without overlapping, where one nontarget video can contain several nontarget trials. Thus, 100 target trials from 100 target videos and 521 nontarget trials from 100 nontarget videos were extracted. The signals for each trial were 1500 ms. The size of the single-trial sample was 16 × 150 (channels × time sample points).Since a domain adaptation network was applied to predict the detection performance. Single-mind signals and multi-mind signals were, respectively, used to construct the source domain and the target domain.K-means distance-clustering method with two clustering centers, 29 maps were clustered into two groups with strong P3 maps and weak P3 maps [Single-mind signals from 29 participants were employed to construct the training set. In our previous studies , individ P3 maps . SubsequμV were regarded as valid signals; otherwise, they were regarded as invalid signals. Thus, each single-trial EEG signal corresponded to two labels  for each participant.Multi-mind signals were used as the testing set. Using the ERP template constructed from the source domain, there were 621 aligned trials in total  available for each individual, which constituted an imbalanced dataset. The size of the single-trial sample was 16 × 100 (channels × time sample points). The validity of the single-trial signals was tested to screen some samples as target domain for domain adaptation network. The threshold value method was adopted for the sample screening. The single-trial signals with maximum amplitude values within ±120 Aimed at enhancing the performance of group detection of dynamic visual targets, MLDANet is proposed as shown in In the proposed framework, an unsupervised single-source domain adaptation network with strong P3 map individuals as the source domain for dynamic visual target detection (P3-sSDA network) is used as the individual network unit . The P3-N target domain individuals from one group with N P3-sSDA networks, which were used as classifiers that synchronously worked on predicting the binary classification probability of single-trial signals. Collaborative decision-making was achieved by the decision-making fusion. The mutual learning strategy was introduced between N P3-sSDA networks and collaborative decision-making. Data from the common source domain and different target domains were, respectively, denoted as S0, T1, T2,…, and TN, where N P3-sSDA networks shared the same source samples and used N different target domain samples. For a single P3-sSDA network, the input sample number of source domain or target domain was named as batch size m. For the n-th target domain individual, m source domain samples x1s, x2s,…, xms and m target domain samples x1tn, x2tn,…, xmtn were input into the n-th P3-sSDA network in each batch. Importantly, target domain samples from N target domain individuals were synchronously recorded for the same stimulus scene. Thus, the prediction category labels of the target domain could be shared among N P3-sSDA networks, which was crucial to achieve the information interaction. For each iteration, the P3-sSDA network could output the domain discriminant probability between source domain samples and target domain samples, the category prediction probability of source domain samples, and the category prediction probability of target domain samples. These probabilities were, respectively, denoted as pnd, pns, and pnt for the n-th P3-sSDA network. Since N individuals synchronously received the same stimuli information, the prediction probability, p1t, p2t,…, and pNt, could reflect the discrimination level for the same information from different individuals. In the process of domain adaptation, the category labels of the source domain ls and the domain labels ld were available; hence, the category loss of the source domain was given asn-th target domain, La  dvs,tn, could be obtained for the n-th target domain:In the MLDANet, there were lt, which would be estimated in each iteration. By averaging the individual predictions, the integrated prediction probability pt was binarized as lt:lt was used as the pseudo-label and synchronously fed back to N P3-sSDA networks to calculate the category losses of target domain {Lclasstn}n=1N.Nevertheless, the category loss of the target domain was unknown due to the lack of category labels of the target domain N P3-sSDA network, the entire adversarial learning problem could be described as follows:La  dvs,tn, Lclassstn, and Lclasstn denote the domain discrimination loss between the source domain and the n-th target domain, the category loss of the source domain when adapted to the n-th target domain, and the category loss of the n-th target domain, respectively; α, γ, and β are hyperparameters which, respectively, denote discrimination loss weight, category loss weight of source domain, and category loss weight of target domain.Thus, the category and discrimination losses could be calculated. For the MLDANet with ld and ls, but also refers to the collaborative label lt, which is calculated from all individual networks. By the backpropagation of collaborative label lt, all the individual networks can learn from each other and make common progress. This process can help small network training to be more powerful. Different from classical cBCI with once collaborative decision-making, with the iteration and updating of network parameters, the dynamic learning ability of the individual network was established in the MLDANet. Thus, the single P3-sSDA network  could learn from the source domain, target domain, and collaborative decision-making (group). After the training process of DA, the online testing can be conducted as the procedure of red dotted line in The mechanism of information interaction among multi-mind signals was established through information integration and feedback. In the MLDANet framework, each individual network not only receives the supervision from individual network labels, sub6, sub11, sub12, sub13, sub14, sub16, sub17, sub19, sub20, sub21, sub23, sub26, sub28} and a weak P3 group {sub1, sub2, sub3, sub4, sub5, sub7, sub8, sub9, sub10, sub15, sub18, sub22, sub24, sub25, sub27, sub29}. The topographies of the strong P3 group and the weak P3 group at the P3 peak value are presented in A total of 29 individual P3 maps were clustered into a strong P3 group {In this work, we compared the detection performances of four BCI frameworks, namely, the single-mind BCI (sBCI), the single-classifier cBCI (SC-cBCI), the multi-classifier cBCI (MC-cBCI), and the proposed MLDANet-cBCI framework. The summary of these BCI frameworks is shown in The optimal parameter values are shown in The detection performances of different BCI frameworks are shown in p < 0.01), and could even exceed the group performance in the SC-cBCI framework (0.59) and the MC-cBCI framework (0.61)  . This fiIn order to achieve a better detection performance, the optimal number of source domain individuals was evaluated on different BCI frameworks. According to the previous work, source domain individuals with stronger P3 maps contribute to better detection performance . When thIn the present work, we developed a multi-mind cBCI framework to enhance the group detection performance of dynamic visual targets. In this framework, a mutual learning domain adaptation network (MLDANet) was proposed to establish the mechanisms of information interaction and dynamic learning between individual network units and collaborative decision-making. By a mutual learning strategy, the collaborative decision-making could guide the re-decision-making process of the individual network for better and more robust detection performance. The results indicated that the proposed MLDANet-cBCI framework outperforms the other cBCI frameworks with the highest F1 score, 0.73, and classification accuracy, 0.91, when three participants collaborate. The mutual learning strategy can effectively improve the individual network capability. Therefore, the proposed cBCI framework provides a novel multi-mind collaborative mode for the improvement of collaborative work performance, which is of great significance for the progression of research on human augmentation.


We investigated the wetting transitions of tetradecane and hexadecane droplets in dodecyltrimethylammonium bromide (C12TAB), tetradecyltrimethylammonium bromide (C14TAB), and hexadecyltrimethylammonium bromide (C16TAB) aqueous solutions. By varying the surfactant concentration, the formation of mixed monolayers of a surfactant and an alkane was observed at the air–water interface. Depending on the combination of surfactant and alkane, these wetting monolayers underwent another thermal phase transition upon cooling either to a frozen mixed monolayer (S1) or a bilayer structure composed of a solid monolayer of a pure alkane rested on a liquid-like mixed monolayer (S2). Based on the phase diagrams determined by phase modulation ellipsometry, the difference in the morphology of the nucleated S1 and S2 phase domains was also investigated using Brewster angle microscopy. Domains of the S1 phase were relatively small and highly branched, whereas those of the S2 phase were large and circular. The difference in domain morphology was explained by the competition of the domain line tension and electrostatic dipole interactions between surfactant molecules in the domains. It is well known that the 2D analogue of surface tension, called line tension, arises at the boundary between two surface phases. Line tension has been discussed in its relation to the lipid raft formation in cellular membranes ,2,3,4. OOn the other hand, monolayers of surfactant molecules adsorbed at the air–water interface have 2D gas (G), liquid (L), and solid (S) phases, similar to 3D materials, distinguished by the abrupt change in surface density observed when the surfactant concentration or temperature is varied. Among these surface phases, only sparingly water-soluble amphiphiles, such as long-chain alcohols, show a 2D solid phase. This is because ionic surfactants and nonionic surfactants with large hydration shells generate in-plane repulsions between their hydrophilic groups, therefore hindering the formation of highly condensed films.However, as we showed previously ,9,10, sun-alkanes of various chain lengths in aqueous hexadecyltrimethylammonium bromide (C16TAB) and showed that an S2 film formed for octadecane and longer alkanes, while for alkanes with chain lengths similar to or shorter than C16TAB, S1 film formation dominated. They also applied X-ray reflectometry to determine the molecular-level structures of these surface frozen films.Deutsch et al.  studied The type of surface frozen phase can also be determined by ellipsometry because the coefficient of ellipticity obtained for the S1 and S2 phases is largely different. Using this technique, we created a 2D phase diagram for the wetting films of tetradecane (C14) in tetradecyltrimethylammonium bromide (C14TAB) aqueous solution and hexadecane (C16) in dodecyltrimethylammonium bromide (C12TAB) aqueous solution as a function of the temperature and surfactant concentration in the aqueous phase ,9. The SIn this paper, we performed ellipsometric measurements to construct 2D phase diagrams for six combinations of alkanes C14 and C16) and surfactants . We made these selections because surface freezing for shorter-chain alkanes is only observed in a supercooled state, and there is a solubility limit for longer-chain surfactants. In addition, based on the obtained 2D phase diagrams, the morphology of the nucleated S1 and S2 domains in the liquid-like mixed monolayer (L) was investigated by using Brewster angle microscopy (BAM). The size and shape of domains were determined by line tension and electrostatic interactions between dipoles on cationic surfactant head groups. The former favors a circular domain with minimum line energy, whereas the latter favor smaller and elongated domains ,14. Comp and C16 n-Tetradecane  and n-hexadecane  were distilled under reduced pressure before use.Dodecyltrimethylammonium bromide , tetradecyltrimethylammonium bromide , and hexadecyltrimethylammonium bromide  were purified through recrystallization from a mixture of acetone and ethanol. Oil-soluble impurities were extracted from their solid powders using hexane. The purities of all the surfactants were confirmed by the absence of a minimum on the surface tension vs. concentration curves around their critical micelle concentrations (CMCs). All samples were prepared with Milli-Q water. Ellipsometric measurements were performed using a Picometer Ellipsometer  equipped with a HeNe laser , a Langmuir trough was first filled with the surfactant solution. After the liquid alkane was spread on the solution surface, in keeping with the ellipsometric measurements, the temperature of the Langmuir trough was continuously decreased to capture the subsequent images of surface freezing processes. The temperature of the solution was monitored using a Pt resistance thermometer during the BAM observation, with a precision of 0.1 K.−1.We also performed surface tension measurements for the C14TAB-C14, C16TAB-C14, and C16TAB-C16 systems to determine the surface density of surfactants in the L and S1 phases. To measure the surface tension of surfactant–alkane mixed adsorbed films, pendant drop measurement was conducted in a closed glass cell saturated with alkane vapor. The experimental error in the interfacial measurements was <0.1 mN mnterface . For thed and permittivity ε. In this case, d = 1.38 nm determined previously by X-ray reflectometry [−3 for the C16TAB + C16 system. In order to calculate When we measured equation ,17,18:(1ε= 2.05)  and d = ctometry , ρ¯L is d = 2.17 nm [−3, which is in good agreement with the −3). In actuality, the On the other hand, the frozen monolayer (S1) is optically anisotropic, and the Drude equation can be rewritten as :(2)ρ¯S=π crystal ,21 and d 2.17 nm , EquatioWe repeated the same experiments at various surfactant concentrations and summarized the obtained data as temperature–surfactant concentration diagrams . CompariThe results of the BAM measurements are summarized in Contrary to S2 domain formation, the structures observed for the S1 domain were more complicated. In the C14TAB-C14 system, we first observed a network of thin S1 domains that evolved into a thicker stripe with decreasing temperature. When the C14TAB concentration was increased, the width of the stripe domain increased. The boundaries between the S1 domain and its surrounding L phase also had spike shapes, which were not observed in other S1 domains. For example, in the C16TAB-C14 system, the S1 domains first appeared as a deformed circular shape. However, the size of the circular domains was much smaller than that of the S2 domain, and, as a result, the number of nucleated domains was also greater than that of the S2 domains. These domains then merged into a larger domain, causing the perimeter to curve in an irregular manner and protrude at some points. Similar behavior was also observed in the C16TAB-C16 system, although the size of the S1 domain looked slightly larger and the curvature of the phase boundary seemed to be less in comparison to the C16TAB-C14 system. Hence, it may be stated that the nucleation behavior in this system is intermediate between the C14TAB-C14 and C16TAB-C14 systems from the viewpoint of their morphologies.τ and the electric repulsions of hydrophilic groups in the solid domain. The most simple expression for domain line tension is given byγ is the surface tension of hydrocarbon chains exposed to the air at the domain boundary (~25 mJ m−2), and Δl is the height mismatch between the solid domain and the surrounding L phase. McConnell et al. [R, where molecular dipoles are oriented perpendicular to the air–water interface, asm is the dipole moment density difference between the domain and its surroundings, As mentioned in the Introduction, the morphology of solid domains can be determined by the competition of the domain line tension l et al. ,24 propol is roughly equal to the all-trans chain length of the alkanes examined (see l~1.9 nm) and C16 (~2.2 nm) S2 domains on the 2D liquid film can be estimated as ~4.8 × 10−11 and ~5.5 × 10−11 J/m, respectively. On the other hand, the opposing electric repulsion term is practically negligible because the S2 domain is composed of an island of frozen alkane molecules floating on the 2D liquid. Therefore, line tension dominates the phase behavior, and the domains become large and circular in order to minimize the energy penalty of the perimeter, as demonstrated in the BAM images taken for the C12TAB-C16 and C14TAB-C16 systems.For S2 phase domains, Δined see , right. l can be estimated as 0.8 nm, and the resultant −11 J/m, which is about 1/2~1/3 compared to that estimated for the S2 phase domains. In addition, this line tension contribution is further diminished by molecular dipole contributions. In the L phase, the trimethylammonium head groups and counterions arrange themselves to minimize unfavorable electrostatic interactions. However, such a rearrangement is difficult in the S1 phase because the chain packing between hydrophobic chains and alkane molecules leads to a coplanar arrangement for the head groups. As a result, all dipoles created between the TMA+ ions and the adjacent Br− ions in the Stern layer are lined up, leading to a large dipole density difference between the S1 domains and the surrounding L phase . In such a case, the electric repulsion exerted on an arbitrary surfactant ion (open circle in We had previously interpreted the domain morphology observed for C14TAB-C14 (S1) and C14TAB-C16 (S2) systems according to the abovementioned concept . In thisConsidering the average chain length of the surfactant and alkane contained in the S1 domain, the magnitude of the line tension seemed to increase in the order of C14TAB + C14 < C16TAB + C14 < C16TAB + C16. For example, the S1 domains that first appeared in the C16TAB-C14 system were small circular ones, which then merged into a larger irregular shaped domain as the temperature decreased. This indicates that the line tension of S1 domains observed in the C16TAB + C14 system was higher in comparison to that of those in the C14TAB-C14 system. This increment in line tension seems to suppress the transformation of the domain morphology into striped domains. However, going by how the size of circular domains was much smaller than that observed for S2 domains, and that the domains eventually grew into an irregularly shaped network, it can be concluded that electric dipole repulsion still dominates the nucleation process on the whole. In the C16TAB-C16 system, the line tension of which is expected to be of the largest value among the three systems, a relatively large domain is formed immediately after the phase transition, although the domain shape is still irregular with flexible curvatures.When the surfactant concentration is increased in the same system, the growth rate of the domain seems to be faster, and large domains can be more easily found under the microscope. As shown in In this paper, we demonstrated that the morphology of nucleated solid domains of surfactant–alkane mixed films is determined by the competition between domain line tension and electric dipole repulsions between surfactant head groups. A small change in the hydrocarbon chain length significantly changed the shape of the S1 domain from small, circular, thin-striped to protruded domains, indicating that the dipole repulsion term dominated the morphology of the domains in the experimental conditions examined here. For ordered domains of lipids, it is believed that the size of the domains is in the range of several tens of nanometers. In order to create such a small domain, it is necessary to reduce the line tension term by a considerable extent. According to this line, similar to surfactants in 3D systems, it has been proposed that some type of molecule acts as a line-active agent (linactant) which stabilizes 2D domains ,27. Stud